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1. Use this command to copy a part of the active view to the clipboard A zoom box is used to select the part to be copied Click outside the view frame or press escape to exit this option Shortcut Keys CTRL L 4 4 Edit Paste command Paste command Edit menu Use this command to paste from the clipboard The clipboard must contain a bitmap If the bitmap is larger than the view it is clipped The zoom cursor is used to set the left top corner in the view where the bitmap will be pasted Click outside the view frame or press escape to exit this option Shortcut Keys CTRL V 4 5 Cubic Values Window Cubic Values Window To support the cubic Mandelbrot formulas g0 thru g9 variables have been added to adjust z origin and magnify the z plane while calculating pixel depth Normally you can keep origin set at 0 0 0 and z mag at 1 0 But these can be useful to tweak in small increments when drawing Mandelbrot quaternions Then a small change in z origin can rotate details on a close up slightly so you can adjust the view accordingly Each shift in z origin will require re zooming to get back to the area of interest The z mag variable makes the z plane non symmetrical pushing up some details while other details recede So it too is useful to change viewpoint The affect on Julia quaternions is less noticeable for z origin shifts You can usually re zoom to produce the same Julia image Cubic Mandelbrots quaternions use the S and Si varia
2. d8 q9 e0 el e2 e3 e4 e5 e6 e7 e8 e9 fo fl f2 B f4 sin z kzn vers z c vers z covers Z C c vers z c vers z covers z c foggy coastline 1 2 c Barnsley foggy coastline 2 2 c Barnsley sin vers c csec z 2 c z 3 sech z 2 c C z c 1 2 2 cos 1 w22 c z e z sqr 2 pi z c 1 8 63z 5 70z 3 15z c Z 2 e z z 1 c z 2 exp z c z 3 c c z 3 sqr 2 pi z c z 2 csc h cot h 4 c 1 sin Z c 3 Z 2 c where x abs real z y imag z Paul Carlson z 2 where x abs real z cr y imag z ci Paul Carlson c cos z c Z COS Z C z 2 z sin z c z 2 z pi c z j z k z 2 1 c z j z 2 z k c z 1 z 2 z c z j z k z 1 c chaos formula Barnsley snowflake IFS Barnsley cos z c z 3 exp z c z c z 1 z 1 c Z 4 c 4 ZN24 Z 3 sin c cos c c z 2 1 cz 2 c 1 z z c c 1 z z z c 1 c z z z 2003 2010 Mystic Fractal Help menu so f5 1 c z z c c f6 1 c z z c c f7 1 z z c c 1 z c 18 1K z z z c c f9 1 z z z z c g0 z 3 3c 2z s cubic Mandelbrot Note 3 gl z 3 3sz c alternate cubic Mandelbrot g2 z 3 3c 27 2 s cubic Mandelbrot variant g3 243 3sz42 c alternate cubic Mandelbrot variant g4 z 3 3c 2 z s cubic Mandelbrot variant g5 z 3 3s z c alternate cubic Mandelbrot variant g6 z 3 3c 3 z s cubic Mandelbr
3. if then endif if argument then phrase endif if argument is true then do phrase else skip phrase then tag is optional but a comma should follow argument or put if argument on separate line if then else endif if argument then phrase else phrase endif if argument is true then do phrase else skip phrase and do alternate phrase then tag is optional but a comma should follow argument or put if argument on separate line O 2003 2010 Mystic Fractal Help menu 72 Note if then endif and if then else endif loops can be nested only when endifs follow each other at the end of the loops For example if argument if argument then phrase endif endif Math operators addition subtraction multiplication division A power function lt less than lt less than or equal to gt greater than gt greater than or equal to not equal to equal to ll logical or Gf arg is TRUK 1 or arg2 is TRUE amp amp logical and if arg is TRUE and arg2 is TRUE Constants and variables complex constant c or C read write complex conjugate cc or CC read only convergence limit cl or CL the constant entered in the Converge gadget read only cr the constant entered in the cr box in the Parameters window use j for parser ci the constant entered in the ci box in the Parameters window use k for parser e eo
4. A random Julia fractal is generated Many of the rendering options of Fractal ViZion are selected on a random basis and the Mandelbrot space for one of the 180 built in formulas is scanned for an interesting Julia set The palette used is also randomized Note In most case the Julia search is a short one but sometimes the seek mode can seem to get stuck when the criteria for an interesting Julia set fails to match the formula used In the latter case either click the left mouse button and restart the search process or pressing a palette key will sometimes override the current search and restart it if HSV filtering has been selected This is like the Random Julia command except that more options are randomized including spin and switch and the Formula Type can be composite or Escher so the search draw time may be somewhat longer and the results not as certain But the images can be quite weird Tip some things remain to be done after the Julia set is drawn The algorithm doesn t check the type of split palette that is used so a mismatch in the Divide by color option may need correcting e g Divide by four may be selected for a divide by eight palette Feel free to experiment with all the parameters reframe the image change palettes etc This routine provides a fast intro to many options in Fractal ViZion that the user may be unfamiliar with no knowledge of fractal science math required Channel ES Random Escher Channel QT butt
5. May 1995 ZPlot 3 1 ZPlot for Windows 3 1 60 built in formulas Added hypercomplex support for most built in formulas May 1997 ZPlot 24 02 first true color version of ZPlot 91 built in formulas Included support for 3D quaternion plots Fractint par frm files Steve Ferguson s filters anti aliasing and Paul Carlson s orbit trap routines June 1997 ZPlot 24 03 added Earl Hinrichs Torus method 2003 2010 Mystic Fractal Help menu os July 1997 ZPlot 24 08 added HSV filtering December 1997 Fractal Elite 1 14 100 built in formulas added avi and midi support March 1998 Split Fractal Elite mto two programs Dreamer and Medusa multimedia April 1998 Dofo 1 0 supports new Ferguson Gintz plug in spec June 1998 Dofo Zon redesigned multi window interface by Steve Ferguson and includes Steve s 2D coloring methods August 1998 Dofo Zon Elite combination of Fractal Elite and Dofo Zon October 1998 Dofo Zon Elite v1 07 added orbital fractals and IFS slide show November 1998 Dofo Zon Elite v1 08 added Isystems April 1999 Split Dofo Zon Elite into two programs Fractal Zplot using built in formulas and rendering methods and Dofo Zon to support only plug in formulas and rendering methods May 1999 Fractal Zplot 1 18 added Phong highlights color formula mapping and random fractal methods June 1999 completed Fractal ViZion first version with autom
6. Mouse Click the minimize icon on the title bar Keys ALT F9 Maximize Command Maximize command System menu Use this command to enlarge the active window to fill the available space Shortcut Mouse Click the maximize icon i on the title bar or double click the title bar Keys CTRL F10 enlarges a drawing window Next Window Next Window command drawing Control menu Use this command to switch to the next open drawing window Fractal ViZion determines which window is next according to the order in which you opened the windows Shortcut Keys CTRL F6 Previous Window Previous Window command drawing Control menu Use this command to switch to the previous open drawing window Fractal ViZion determines which window is previous according to the order in which you opened the windows Shortcut Keys SHIFT CTRL F6 Close Close command Control menus Use this command to close the active window or dialog box Double clicking a Control menu box is the same as choosing the Close command 2003 2010 Mystic Fractal Main Index 4 Shortcuts Keys CTRL F4 closes a drawing window ALT F4 closes the application 1 10 Restore Restore command Control menu Use this command to return the active window to its size and position before you chose the Maximize or Minimize command 1 11 Switch to Switch to command application Control menu Use this command to display a list of all open applications Use this Ta
7. O 2003 2010 Mystic Fractal Help menu 2 k n sets the z angle for 3D curve Notes The color index is initialized at 2 Each index of the current palette is used by the ray tracer as a separate palette so up to 236 different objects can be modeled using up to 236 different colors This works best when the index is a dark color The color will be spread from dark to light when it is used during final ray tracing The angles used in turning commands may be negative as 25 When F or a like drawing movement command is followed by an argument as in F 5 the turtle draws the absolute distance specified in turtle units This may be different from FFFFF since the initial length of the draw vector is 100 An equivalent and faster draw command for FFFFF would therefore be F 500 assuming the length vector was not changed by one of the inc dec commands When the length vector of a line is decreased or increased the width of the line is proportionately changed also to retain compatibility with LParser files Under the extended rule set when line width is changed during drawing Fractal ViZion attempts to smooth out width changes by introducing a gradient or gradual width change while drawing If two or more consecutive commands are introduced that change the line width before drawing only the last width change will have this gradient Syntax errors and assignment errors that occur during runtime are displayed in a messa
8. like J and G except that you choose the target type and beginning parameters This is useful for exploring cubic Mandelbrot sets insofar as you can scan the complex c planes for interesting variations Also works for other multi dimensional Mandelbrot formulas that are dependent on the c planes Hint turn off the Image Auto Redraw option after drawing the mapping picture You can then set the target set Mandelbrot quaternion etc before using this key sequence without erasing the mapping picture Shift D use the mouse to examine pixel depth in a drawing By clicking with the left mouse button on any area in the current fractal the pixel s depth and bailout values are displayed in the status bar along with the pixel s coordinates Useful to locate Mandelbrot islands while zooming on an image Click on the title bar or press Esc to exit this command Shift F generate a Julia set from a formula s MandelbrotP space Random points in a formula s current Mandelbrot space are scanned for an interesting Julia Shift Z zoom in out coordinates Like the menu command except does not immediately redraw the picture This allows you to zoom into another screen sector without erasing the previous picture O 2003 2010 Mystic Fractal Fractal Zplot Application Help 8 4 Shift T annotate a picture with text Cursor changes to a crosshatch which you position over the area where you want the text to start Then click the left mous
9. solves Newton Halley transformation of logz c e7 solves Newton Halley transformation of exp z c e8 solves Newton Halley transformation of z c z 1 z 1 for Mandelbrot or Julia set e9 solves Newton Halley transformation of z c z c z 2 c 2 z 4 c 4 f generalized form of Earl Hinrichs sophomore sine function ssin limit fn z s si where fn z finl x n2 y fl c 2 1 cz 2 variant of p4 f2 Gallet 4 01 from Sylvie Gallet s extensive Internet collection Note 16 13 Gallet 4 02 from Sylvie Gallet f4 Gallet 6 01 from Sylvie Gallet f5 Gallet 6 02 from Sylvie Gallet f6 Gallet 6 03 from Sylvie Gallet f7 Gallet 6 04 from Sylvie Gallet f8 Gallet 6 05 from Sylvie Gallet f9 Gallet 7 01 from Sylvie Gallet g0 z 3 3c 2zes cubic Mandelbrot Note 17 gl z 3 3sz c alternate cubic Mandelbrot g2 z 3 3c 27 2 s cubic Mandelbrot variant g3 z 3 3sz 2 c alternate cubic Mandelbrot variant g4 z 3 3c 2 z s cubic Mandelbrot variant g5 z 3 3s z c alternate cubic Mandelbrot variant g6 z 3 3c 3 z s cubic Mandelbrot variant g z 3 3s z 2 c alternate cubic Mandelbrot variant g8 z 3 3c 2 z s cubic Mandelbrot variant O 2003 2010 Mystic Fractal Fractal Zplot Application Help g9 z 3 3s z c alternate cubic Mandelbrot variant hO O C4 1 C O c octonion set Note 4 hl cO CC 1 C O octonion s
10. Cutoff needs to be a small negative value usually equal to the magnify value times the number of color splits E G for a magnify value of 1 you should use a cutoff value of 8 for a divide by eight palette An incorrect cutoff value will cause the colors to overlap in the bubbles For split palette pictures the colors are divided according to their level index as in Indexed Linear 6 The color ranges should be graded from light to dark to highlight the bubble centers Decomposition Decomposition When a Decomposition flag is set you have the option of performing either a binary or continuous decomposition Toggle the External Internal option for either an external or internal decomposition The Angle Only option excludes the Coloring scaling options from consideration when plotting points derived from decomposition It also excludes escape times in connection with the Angle Iteration option on the Color Scaling menu An external decomposition decomposes points that are outside the complex set An internal decomposition decomposes the complex set For Mandelbrot Julia curves z arg is broken into two parts for a binary decomposition For Newton Renormalization curves the binary decomposition is also related to the number of solutions a formula has if it supports mapping option 1 Continuous decomposition breaks z arg into n parts where n angles 2 256 as set in the Continuous Decomposition window Note With the graded palette option c
11. Hj is set to 2 0 and the lighting is set for optimum viewing This option uses an extended set of formulas not all of which may produce useable images all the time The images can be quite different from the traditional quaternion Note for some images an hj value of 2 0 may result in a partially clipped image Sometimes it helps to increase this value to 2 5 or 3 0 but too high a value may interfere with Solid guessing 2 23 Channel C1 Random Cubic Mandelbrot Channel C1 button A random cubic Mandelbrot fractal is generated Like the inverse of Random Julia the essential cubic parameters are randomly adjusted to point into the four dimensional formula GO and then the Mandelbrot set is scanned to find an interesting area to zoom into The ranges are reset and the lighting is set for optimum viewing 2 24 Channel C2 Random Cubic Mandelbrot2 Channel C2 button A random cubic Mandelbrot fractal is generated Like the inverse of Random Julia the essential cubic parameters are randomly adjusted to point into the four dimensional formula GO and then the Mandelbrot set is scanned to find an interesting area to zoom into The ranges are reset and the lighting is set for optimum viewing This option uses the cubic formulas GO and Gl with relaxed parameters to create cubic Mandelbrot like fractals that may extend to six or more dimensions 2 25 Channel CJ Random Cubic Julia Channel CJ button A random cubic Julia fractal the Ju
12. Imag An exclude value of 2 is also used The Map and exclude values are extra parameters that Paul uses in some of his formulas and may be omitted in other cases This is easily done by first 2003 2010 Mystic Fractal Fine Tuning menu s enabling the Carlson extensions by checking the box and clicking on Okay then opening the window again and un checking the box and changing the appropriate variables flags 5 10 1 Orbit trap values Orbit Trap Values Enter a value for Epsilon and Epsilon2 which are used to define the size of the orbit trap areas 001 2 0 and 0 0 epsilon The exclude box is used to exclude the first iterations 0 99 from orbit trapping Click on Apply to apply changes without closing the window Click on Okay to close the window and apply changes if any Click on Cancel to exit the window without changing parameters Epsilon2 is used to create windows into the stalks The default value is 0 0 which produces solid stalks Epsilon2 has no effect on the Petal method Check Carlson extensions to apply additional options that are used in Paul Carlson s 3D like orbit trap methods 5 11 Draw command Draw command Use this command to draw or redraw the image for the current fractal variables Clicking inside the draw window with the left mouse button stops all plotting Use the Continue command to restart plotting from the current column When the Isystem option is selected a custom window is opened to
13. Inc Redwood City California 1989 Wegner Tim Tyler Bert Peterson Mark and Branderhorst Pieter Fractals for Windows Waite Group Press Corte Madera CA 1992 Wegner Tim and Tyler Bert Fractal Creations Second Edition Waite Group Press Corte Madera CA 1993 Whipkey Kenneth L and Whipkey Mary Nell The Power of Calculus John Wiley amp Sons New York 1986 Open Avi Stream Open Avi Stream Through a series of windows this allows you to name and open an avi animation stream and choose a compression method After using the file requester to name the file you are given a choice of compression methods The compression methods include Intel Indeo Video Microsoft Video 1 and Cmepak Codec by Radius All compression methods degrade the original images some more than others The first key frame in the stream is then drawn and written to the file Notes after the stream is opened the size of the fractal that can be drawn is fixed at the size of the frame No changes can be made to the size until the stream is closed New If you open a video stream after setting up a batch mode Demo menu then the frames will be written as a series of bmp obj or wrl files depending on whether AVI Object or AVI WRL is also checked 2003 2010 Mystic Fractal Help menu o 8 9 Write Frames Write Frames With this option frames are written to a stream based on the difference between the current key frame
14. all pixels are interpolated except the first and last colors At 0 no pixels are interpolated Test 2 measures the difference in the sum of the RGB values of adjacent colors If the sum is greater than a preset limit 0 765 no interpolation is done These two tests can be combined with the Both option 4 14 Edit Text command Text Edit menu Allows you to edit text and font and apply it to a drawing Select the font button to set the font style size and color In the text window click on Okay to add a line of text to the current image You can add multiple lines of text too up to 80 characters The cursor will change to a crosshair Position the cursor where you want the text to start and left click the mouse Note font and title text are saved in the file prefs txt in Fractal ViZion s startup directory Title text can also be edited as a single line only in the Edit Formula window 4 15 Preferences Preferences Edit menu Each time you use the Reset command Fractal ViZion restores data variables to built in defaults The Set Defaults button allows you to change some of the data variable defaults to whatever the current settings are Some of the customizable variables include step fine formula viewpoint lighting rotational angles Phong and x y space Iterations Type Constants and a few other variables are excluded to maintain compatibility with the G command The new Reset defaults are O 2003 2010 Mystic F
15. default is 0 Used preceeding a rp command to allow the repeat loop more flexibility in deciding when the beginning postition has been reached Some 3D curves require a loosening of the boundary for the rp loop to work Higher boundary values make the rp loop more effective though too high a value can result in premature bailout To eliminate endless rp loops a failsafe bailout is set at 50000 reps 1 n skip n segments in 3D curve default 0 Use to speed up drawing by decreasing segment resolution Sharp angles may appear as disks rather than a continuous form when segments are skipped In set starting angle for 3D curve default is 0 Using T and r n different part of the 3D curve can be drawn The rp command automatically sets to 0 P set center position for 3D curve Uses the current turtle position as a center point for 3D curves x formula set x formula for 3D curve Can use any trig function plus the angles x y and Z and the loop variable d The default x formula is sin x d cos y d y formula set y formula for 3D curve Can use any trig function plus the angles x y and Z and the loop variable d The default y formula is sin x d sin y d w formula set z formula for 3D curve Can use any trig function plus the angles x y and Z and the loop variable d The default z formula is cos x d u n sets the x angle for 3D curve v n sets the y angle for 3D curve
16. edit fractal variables 24 edit Isystem axiom 27 edit Isystem rules 27 edit octonion parameters 30 edit orbits 28 edit parameters 24 26 edit paste 20 edit preferences 34 edit quattrap 33 edit ray tracing variables 29 edit rgb thresholds 34 edit size 33 edit text 34 edit undo 19 exit 18 F files load palette 17 files load palettes 17 files managing 15 16 17 18 files save palettes 17 H help about fractal zplot 96 help bibliography 92 help built in formulas 73 39 help help help help help help channels 5 chronololgy 97 hot keys 69 parser info 71 remote 5 tutorial 68 image auto alert 36 image auto remote 37 image auto time 36 image clear 37 image continue draw 57 image draw 56 image draw Isystem 56 image pilot 61 image redraw 37 image reset 66 image show picture 57 image new view on zoom 66 map map map map map map map map map lt abs z real or abs z imag 51 gt abs z real or abs z imag 51 abs z 52 abs z imag 50 abs z real 50 abs z real abs z imag 51 z imag 49 z real 49 z real z imag 50 P palettes selecting 42 pixel pixel pixel pixel pixel pixel pixel invert 59 invert off 59 phoenix 63 solid guessing 66 symmetry 64 torus 48 torus off 49 2003 2010 Mystic Fractal Index 102 R render add noise 53 render anti alias 43 render atan co
17. etc for orbit trap pictures that require a reversed palette Neg Button Neg button Use Neg to create a palette that is the complement of the current palette Map Button Map button In Fractal ViZion colors do not cycle smoothly when you adjust the RGB HSV sliders This would be too slow with true color The Map button is used to map color changes to an image after you are done adjusting the sliders H R Button H R button Change from HSV to RGB mode or back In the HSV mode color spreads are based on HSV values instead of RGB values which in some cases results in brighter color spreads 2003 2010 Mystic Fractal Edit menu 32 4 10 5 Spread Button Spread button Select Spread to define a smooth spread of colors from the current spot to another spot in the palette 4 10 6 Copy Button Copy button Select Copy to copy any color to another spot in the palette 4 10 7 SRG Button SRG button Use SRG to switch the red and green components of all palette colors RGB mode only 4 10 8 SRB Button SRB button Use SRG to switch the red and blue components of all palette colors RGB mode only 4 10 9 Okay Button Okay button Click on Okay to exit the palette editor applying unmapped color changes to picture if color cycling is enabled 4 10 10 Reset Button Reset button Use Reset to reset the colors of the palette in use to where it was before it was cycled or modified Note if you change palettes with one
18. ray tracing algorithms to Dirk Meyer for his Phong shading algorithm to Piet van Oostrum for his T2MF without which the midi support would still be a far off dream and to David Makin for sharing his ideas on quaternion colorings and 3D insights Thanks also to Francois Guibert for his Perlin Noise example A special mention for Stig Pettersson for his ground breaking work in cubic Mandelbrots giving me clues to an historic fractal world I hardly knew existed The multi windowing interface in Fractal ViZion is courtesy of that extraordinary and prolific fractal programmer Steven C Ferguson whose filters I have also included in FV Steve s contributions to the look and feel of Fractal ViZion and previous versions of my program have had a deep impact on my fractal imaging experiments For a short history of the programs leading up to this program see Chronology Chronology Chronology History of this program In September 1989 I first had the idea for a fractal program that allowed plotting all complex functions and formulas while attending a course on College Algebra at Lane College in Eugene Oregon In November 1989 ZPlot 1 0 was done This Amiga program supported up to 32 colors 640X400 resolution and included about 30 built in formulas and a simple formula parser May 1990 ZPlot 1 3d added 3D projections for all formulas in the form of height fields May 1991 ZPlot 2 0 first 236 color version of ZPlot for Windows 3 0
19. routine to limit the basins of attraction to viewable 3D areas for formulas that use Newton s or Halley s method etc This method also works for escape time formulas though slower and requiring more iterations to bring out detail When you click on Okay the quaternion generator looks at the Fun 1 gadget in the New Formula window If this contains a preset variable that function is iterated for its escape time then the results are ray traced in any 3D object that may be created Ifthe Type is set to 9 any custom formula Fractint style as in z z3 c in the Formula box is used Not all functions may produce a usable 3D object with this method but it s interesting to experiment with The Quaternion option works for both Mandelbrot and Julia sets depending on which type is selected The Slice variables may be altered to display different 3 D planes of the quad set The Plane variables B Back F Front and P Position allow you to flatten part of the quaternion figure For normal plotting these variables default to 0 To have any effect on the image the Back variable must be different in value from the Front variable The difference between back and front variables determines where the image is flattened These variables are limited to 9 99 with normal values being in the range z to z The position variable sets the color of the flattened plane Axiom Window Axiom Window Enter the basic angle 0 5 360 This angle will be us
20. x 2 y 2 j 2xy k when x gt 0 else x 2 y 2 c jx 2xy kx k Barnsley Note 1 p9 z 2 cz 34c q0 Qz 3 cy z2 ql 2743 c 3z42 1 q2 Newton s method applied to exp z c q3 Newton method applied to sin 2z c q4 Newton s method applied to sin3z c q5 Newton s metod applied to sinz cosz c q6 Newton s method applied to exp z sinz c q7 Newton s method applioed to exp sinz c q8 Newton s method applied to fn z c q9 Newton s method applied to fn z fn z c r0 z43 conj z c c rl z zez 3 c I2 z 3 zec r3 z 2 exp z c r4 z 2 c z 1 r5 cz 34c r6 z 2 cexp z c r sin z cz2 c O 2003 2010 Mystic Fractal es Fractal Zplot Application Help r8 z 1 c when x gt 0 else z 1 cc Barnsley r9 z 1 c when kx jy gt 0 else z 1 c Barnsley s0 sin z c2 sl z4 exp z c s2 c Z424 1 2 z42 1 s3 z 24tan z c s4 strange attractor IFS s 1 4142 Barnsley s5 z 5 c 4 s6 composite function cz c z amp amp z 24c s7 l z24c s8 z 343 c 1 z c 1 c 2 s9 z z 54c 2 t0 z z 64c 2 tl z 7 z 54z 3 z c t2 z 4 z 2 c t3 z 3 tanz c t4 z 2 z c c t5 z 3 c z c t6 discretizes Volterra Lotka equations via modified Heun algorithm t7 z 3 c z c t8 Quaternion set q 24c 2 t9 z 2 cz 2 c u0 Mandelbulb sine based non trig version Note 21 ul Mandelbulb cosine based non trig versio
21. 0 9 j alternate cubic Mandelbrot mapping Therefore an arg value of 3B uses the union of M and M and b real as the fourth dimension Formula Window Formula Type Window Fun 1 and Fun 2 are combo controls for entering selecting up to two formulas either from their drop down lists or in the custom form of Z AZ BZ c Z is the complex variable or function c is the complex constant and A and B are optional real constants There are additionally a Type control an Arg control and an Arg Limit control that determine how the above formulas are processed Note when the fractal type is quaternion custom formulas are only processed through the Fun 1 or the Formula box The Fun 2 combo only uses the built in formulas in its drop down list The Type control accepts a value of 0 to 11 For a value of 0 the first formula is always used and the second formula is ignored For a value of 1 the second formula is processed and the first formula is ignored Type 1 is of use only if you are switching between two functions and don t want to reenter them each time you plot the other one For a value of 2 the first formula is processed if the real component of Z is greater than 0 else the second formula is used O 2003 2010 Mystic Fractal Edit menu 22 For values of 3 the first formula is processed and its output becomes the input of the second formula which is then processed Type 4 takes the average of Fun t1 and Fun 2 Type
22. Low Linear mapping of reversed level potential Ray Trace Ray trace 3D plot Sea Level Set sea level at ground zero 5 7 1 1 Escape Escape Five options are included that color a point based on its escape time when it blows up Escape time coloring The Iteration option uses only the point s escape time The Iteration option uses the sum of a point s escape time and the value chosen which can be picked from a menu that mirrors the Map menu A window is opened to set a q factor 1 200 which scales the sum value The Iteration option uses the product of a point s escape time and the value chosen A window is opened to set a q factor 1 200 which scales the product value 2003 2010 Mystic Fractal s Fractal Zplot Application Help 5 7 1 2 5 7 1 3 5 7 1 4 The Angle option use the absolute value of a point s exit angle theta This is the atan method in Fractint The Angle Iteration option uses the angle formed by the difference between a point s last two exit values and subtracts the point s escape time Using the Angle Only option on the Decomposition menu escape times are not subtracted from the difference angle This is Paul Carlson s atan method Level Level A point is colored based on its logarithmic escape A window is opened to set a q factor which controls the smoothness of picture color A higher q factor results in grainier pictures and excess detail Too low a q factor results in
23. Most of the built in functions except for real Newtons and the Gallet formulas have hypercomplex extensions when values of cj ck hj or hk are non zero Note 11 Hypercomplex Newton Halley maps use only type 2 and type 3 convergence tests Note 12 The default version of hypercomplex conjugate is defined as conjugate h hr hi hj hk A variant of the hypercomplex conjugate uses an arg limit with a non integral value e g 2 1 This makes all imaginary components of h negative such that conjugate h hr hi hj hk Note 13 The formula for a first degree Laguerre polynomial is e t d dt t e t 2d dt t t Note 14 With a non integral value entered in the limit gadget an alternate Fractint version of this formula is executed Note 15 For real Newtons the function selected from the f1 f4 boxes is a real function For a real conjugate the negation of the real term is used Note 16 formulas by Sylvie Gallet have been modified to allow both Mandelbrot and Julia sets to O 2003 2010 Mystic Fractal Help menu 36 be drawn from them Except for Gallet 6 02 the bailout is set with the built in variable zlimit in the Parameters window Gallet 6 02 uses the complex constant p3 limit and converge for bailout Note 17 For the traditional cubic Mandelbrot example in The Science of Fractal Images hj hk cj and ck hypercomplex components of z and c should be set to zero when used with the quaternion type Cubic Mandelbrots qua
24. Replaces the currently selected palette with the palette in F11 Useful when you want to make a palette file pl from the palettes in a lot of individual bitmap files Use the copy data and paste data commands to move the palette from another drawing window into F11 Select the palette CtrH F1 CtrH F9 CtrHF12 CtrkH 0 CtrH 9 you want to move CtrHF11 into then press Tab Hint you can copy data from and to the same window to move the currently selected palette into Ctrh F11 up arrow forward cycle colors one step including set color useable during plotting down arrow back cycle colors one step including set color useable during plotting Shift B erases the 3D background leaving the 3D plot intact Shift C clear the screen to the current background color O 2003 2010 Mystic Fractal Help menu 70 Shift P grab point from Mandelbrot set real and imaginary parts and put values in complex constant Cursor changes to a cross hatch which you position over the area of the Mandelbrot set of interest Then click the left mouse button to transfer the pixel s coordinates to the c constant Click outside window or in window frame to exit routine without grabbing a point Shift J like P except that a Julia set is drawn immediately in sector 2 at size 100 and with iterations of 100 This is a fast exploratory routine for finding interesting Julia sets that can also be used where the Mandelbrot set is discon
25. Use ctrl enter to terminate a line in the formula box An optional bailout routine may be entered as a phrase at the end ofthe formula If the bailout phrase equals a value other than TRUE during iteration the iteration loop is exited There are other flags such as Convergence and Biomorph if set that can force exit also The arg control is limited to 25 characters The Title text box is used with the hot key T to annotate a picture with text Use the Edit Text O 2003 2010 Mystic Fractal Edit menu 24 command to change font text color or format text into multiple lines Text in this box is not saved in a picture s data file but once entered the same text can be used over and over for different pictures Useful for adding copyright author info to batches of pictures Since the same title text may be used many times it is shared among views and saved in the file prefs txt in Fractal ViZion s startup directory Click on the Apply button to use the formulas currently displayed in the window Use the Okay button to apply the formulas and close the window or use Cancel to exit the window without making any changes or cancel current changes Ifchanges have been applied before clickmg on Cancel then the formulas will revert to the state when the window was last opened Note commands exterior to this window as in the Demo menu may cause the window to be closed and reopened with new values In this case Cancel only returns the form
26. a point takes to converge according to an alternate formula described by C Pickover in Computers Pattern Chaos and Beauty 4 if the Arg Gadget is set to 4 a merging of methods 1 and 3 After the point converges according to the alternate formula 3 its roots are colored according to 1 5 if the Arg Gadget is set to 5 a variation of method 1 with double convergence checking inside the loop 6 7 and 8 alternate convergent formulas 9 a variation of method 3 with double convergence checking Note 5 An additional third argument that affects the convergence speed of Newton Halley maps may be one of the following six methods T relaxed Newton method uses the formula z z sf z f z m modified Newton transformation uses the formula z f z f z si Note Si here references the s variable 1 not the complex variable s si d relaxed modified Newton method uses the formula z sf z f z si p premodified Newton transform uses the formula sz f z f z c complex Newton transform uses the formula z f z f z c where c is the complex constant n Nova variation by Paul Derbyshire z f z f z c The s constant is entered via the S gadget Note 7 the term fn w represents any one of 47 user defined functions chosen through the f1 f4 gadgets 0 sin w 1 smh w 2 cos w 3 cosh w 4 tan w 5 tanh w 6 exp w 7 In w 8 w c 9 w z 10 1 w 11 w 2 12 w 3 1
27. any color to another spot in the palette Select Spread to define a smooth spread of colors from the current spot to another spot in the palette Copy and Spread take effect immediately when you select another spot with the mouse button You can cancel the operation with the Cancel button In Fractal ViZion colors do not cycle smoothly when you adjust the RGB HSV sliders This would be too slow with true color The Map button is used to map color changes to an image after you are done adjusting the sliders In the HSV mode color spreads are based on HSV values instead of RGB values which in some cases results in brighter color spreads Right click on any point on the main window and the palette color for that pixel will be displayed in the palette editor You can use any of the color cycling keys after clicking on the main window to see the effects of the cycling in the palette editor window Note color cycling and color selection from pixel only works when the image has been drawn in the current session If you load a pre existing image file you must redraw it to cycle colors etc Anti aliasing 3D height fields undoing an action and hsv filtering also disable color cycling Use Reset to reset the colors of the palette in use to where it was before it was cycled or modified Note if you change palettes with one of the function keys any modifications to a previous palette 2003 2010 Mystic Fractal 31 Fractal Zplot Application He
28. character by character For those who are not familiar with L systems a discussion of their basic features and how they differ from other turtle graphics is a good starting point Lsystems have as their base an axiom which is a string of character commands or a single character The character can be a command in itself such as F for forward or it may be a production rule which is a string of commands also The axiom and production rules are created and edited with separate editors When the axiom is run the axiom is scanned for commands and or rules Recursion is used to substitute where necessary a production rule string for a single character to the depth specified at runtime In OL systems quite long character strings can be built this way and then executed Once the string is built it is then stripped of non commands and executed without displaying the commands on the screen The size of the drawing object is thus established and it is then scaled and drawn on the screen The first significant difference from other turtle graphics systems is now apparent self scaling The object s will never overrun the screen boundaries Objects can be displayed to the limits of the window regardless of window size Since object size is always relative to the window size a scaling factor is used to create similar objects of different size Other turtle systems would vary the length of an object s sides L systems have a stack available to keep
29. choosing the frame rate 1 60 and using the file requester to name the file you are given a choice of compression methods You can also choose no compression for optimum view quality All compression methods degrade the original images some more than 2003 2010 Mystic Fractal Fractal ViZion Remote ta others The first key frame in the stream is then drawn and written to the file Note after the stream is opened the size of the fractal that can be drawn is fixed at the size of the frame No changes can be made to the size until the stream is closed 2 43 gt button gt button With this option frames are written to a stream based on the difference between the current key frame and the previous key frame The first key frame is written when you open a stream The next key frame is created each time you use this option In between you can zoom or change Fvr variables as much as necessary The stream is only written to when this option is used The last key frame is automatically saved after the tween series is written The number of frames may range from 1 1500 frames between keys With a frame number of 1 only the key frames are written This allows animation to be created that incorporate all scalable variables in Fractal ViZion Use the Cancel button to exit this dialog without initializing a new series of frames Check the Log Scaling box if you want the frames to be written with logarithmic space between frames els
30. color blue slider 33 button 14 color cancel button 32 button 13 los But 32 button gt 14 SO COPY SURON color divide by eight palette 42 color divide by four palette 42 color divide by one palette 42 color divide by two palette 42 color edit palette 30 color green edit box 33 color green slider 33 color h r button 31 color map button 31 color neg button 31 color okay button 32 color pixel 64 color rand button 33 color red edit box 32 color red slider 32 color reset button 32 color reverse button 31 color spread button 32 color srb button 32 color srg button 32 button abot 7 button batch 6 button bmp 13 button channel 10 12 button channel 11 12 button channel 12 12 button channel c1 10 button channel c2 10 button channel cj 10 button channeles 9 button channel hf 11 button channel J1 8 button channel J2 9 button channel LD 11 button channel LS 12 button channel o1 11 button channel 02 11 button channel OR 12 button channel Q1 9 O 2003 2010 Mystic Fractal w Fractal Zplot Application Help colorscaling background 40 colorscaling continuous potential colorscaling escape 38 colorscaling graded palette 40 colorscaling level 39 colorscaling set only 40 colorscaling use level curve 39 colorscaling use palette1 40 D demo batch mode 94 N n edit clip 20 edit copy 19 edit cubic values 20 edit formula 21
31. enter system draw options 5 11 1 Draw Lsystem command Draw Lsystem command The Isystem draw window has edit boxes to set projection angles roll pitch and yaw The angles have a range of 360 to 360 degrees The initial turtle heading is 0 1 0 which moves the turtle up in the direction of the y axis when the projection angles are all 0 The view may be improved when some of the projection angles are non zero or to rotate an object done with LParser to an appropriate viewing angle The skewing angles affect the line styles when the line width is greater than 1 These can warp the lines tubular or poly to a non uniform width The light point is similar to that used when Fractal ViZion draws 3D quaternions The Lighting variables shininess highlight gamma and ambient are used to adjust ambient light and Phong highlights The ranges for these variables appear beside their label Decreasing the shininess value increases light reflected by the quaternion and the apparent sheen on the quaternion s surface O 2003 2010 Mystic Fractal Fractal Zplot Application Help 5 12 5 13 The ambient value controls the amount of ambient light that illuminates the quaternion The highlight value increases or decreases the specular Phong highlighting while the gamma correction increases or decreases the intensity of the light source s illumination Note once a plot has been drawn the lighting variables and light point can be changed w
32. exclusive with the Newton Renormalization and Boundary Scan flags May use Newton display methods 3 and 6 8 alternate convergence tests by setting the arg gadget to these values Default Function Default Function When this option is enabled off by default convergent functions are iterated according to their original type Fractal ViZion allows treating a renormalization curve as a Newton curve or vice versa but the governing flag must be set through the flags menu The Default Function option allows a built in function to work as a Newton or renormalization curve without those flags being set Newton functions work only as Newtons and likewise for renormalization formulas Function types 2003 2010 Mystic Fractal Fine Tuning menu 46 that use two built in functions can distinguish between convergent and non convergent formulas and use the suitable escape or convergent checking for each formula 5 8 10 Level Curve Level Curve Level curves map the set points based on how small the value of Z gets This allows the inside of the complex set to be color scaled Log Map 1 produces colored bands on the inside of the complex set Points are mapped according to what the value of z is at final iteration Small Log 2 and Linear Map 5 produce circular patterns inside the complex set Points are mapped according to the smallest value z gets during iteration Indexed Log 3 and Indexed Linear 6 are mapped according to the time it
33. is mutually exclusive with the Boundary Scan Convergence and Renormalization flags and automatically excludes all points that don t converge to one of the attractors set within the preset number of iterations The points that converge are colored with one of up to 6 possible color spreads the built in functions may allow more colors evenly spaced in the current palette according to the root they converge to and the time it takes to converge The non converging points are mapped with the set color or their level set color with a level flag set after the maximum number of iterations Non converging points show up typically as round areas or spots Generally a limit of 50 iterations gives optimum results The Newton transformation is normally used with Julia sets as the attractors solutions of the formula can be calculated beforehand It s also possible to explore the Mandelbrot set applied to Newton s method but only with some of the built in formulas mentioned above It this case the solutions of the formula for every point on the screen have to be calculated separately which the program does in a dedicated routine 5 8 6 Newton Off Newton Off Turns off the Newton flag otherwise this option is disabled 5 8 7 Renormalize Renormalization The Renormalization flag uses a hierarchical lattice transformation to map magnetic phases with either the Julia set or Mandelbrot set as the iterated function Consult The Beauty of Fractals by
34. is similar to the difference between hypercomplex quaternions hypernions and quaternions The algebra for octonion and hyper octonions differ in how they conform to or fail in the associative and commutative laws Note 20 The timewave array is derived from the formula of Matthew Watkins and Peter Meyer s translation to c In the Julia set version the array acts as a continuously varying complex constant of the form tcl timearray 2 iteration 384 25 tci timearray 2 iteration 6384 1 25 etc In the Mandelbrot version the array acts as an increment to zreal and zimag with initialization being in the same form as the Julia set The divisor 25 was chosen strictly for esthetics as this value enhances the openness of the timewave fractal Note 21 These formulas were designed by Paul Nylander and David White in their search for the true 3D Mandelbrot The non trig versions are limited to exponents 2 to 8 and 2 to 8 inclusive Use the trig based formulas for exponents beyond 8 and 8 or non integral exponents such as 2 5 The non trig versions are approximately 3 4 time faster Enter the exponent in the s box Using negative exponents with the Mandelbulb formulas produces inverted fractals with a large hole in the center of the 3D figure They are very sensitive to bailout magnitude Use a low value such as 4 for best results Since most of the detail in inverted 3D fractals is inside the shell the Dive function is also useful
35. menu Use this command to arrange multiple opened windows in a non overlapped fashion Arrange Icons Window Arrange Icons Command Use this command to arrange the icons for minimized windows at the bottom of the main window If there is an open drawing window at the bottom of the main window then some or all of the icons may not be visible because they will be underneath this drawing window Size DeskTop Window Size DeskTop Command Use this command to size the active drawing window to its frame size Use after Tile command to reduce white space around a drawing that is smaller than screen size 14 2 6 1 2 command Window menu O 2003 2010 Mystic Fractal Window menu s Fractal ViZion displays a list of currently open drawing windows at the bottom of the Window menu A check mark appears in front of the drawing name of the active window Choose a drawing from this list to make its window active 8 Help menu Help menu commands The Help menu offers the following commands which provide you assistance with this application Getting Started Tutorial for new users of Fractal ViZion Index Offers you an index to topics on which you can get help Hot Keys Quick reference to Fractal ViZion s hot keys Parser Info Quick reference to Fractal ViZion s parser variables and functions Built in Formulas Quick reference to Fractal ViZion s built in formulas Bibliography Sources for fractal information and complex numb
36. of menu items as you use the arrow keys to navigate through menus This area similarly shows messages that describe the actions of toolbar buttons as you depress them before releasing them If after viewing the description of the toolbar button command you wish not to execute the command then release the mouse button while the pointer is off the toolbar button The right areas of the status bar indicate which of the following keys are latched down Indicator Description CAP The Caps Lock key is latched down NUM The Num Lock key is latched down SCRL The Scroll Lock key is latched down Phoenix Phoenix The Phoenix flag rotates the planes so that the imaginary plane is mapped horizontally and the real plane is mapped vertically 2003 2010 Mystic Fractal This option is normally used for mapping Phoenix curves Shigehiro Ushiki which are Julia related curves based on the formula f z 1 2 p qz p and q are constants and the Z term of gz is actually the value of z n 1 or the previous value of z before the current iteration zn is reserved by Fractal ViZion to represent this value while the complex constant set in the Parameters window becomes p and q The real part of the complex constant is p and the imaginary part of the constant is q when the Phoenix option is chosen If the Phoenix flag is used with the Mandelbrot option j and k should be used as the constants since the complex constants p and q a
37. repeating graded palette versus the default repeating modulus color scaling Has no effect on the Background or Use Level Curve options or when you use the cutoff value in the Parameters window as a color multiplier When used with the Escape Iteration coloring mode and a negative cutoff value iterations are interpolated to reduce banding in escape time pictures Three options are provided for smoothing The Interpolated version works for most escape time formulas except convergent types Newton and renormalization The Mandelbrot version is based on Linas Vepstas log log algorithm and is designed mainly for formulas that use Z 2 as their main focus such as z 2 c The Exponential smoothing method is based on Ron Barnett s algorithm and works for both escape time and convergent type fractals Level graded coloring 5 7 1 8 Use Palette Use Palette 1 for Background Filter This allows you to use palette 1 with a background filter instead of the default palette to add highlights to a picture When Background filter is checked in the Filter window and a filter is selected FV uses palette 1 for any color indexes modified by the filter This option is not available with solid guessing O 2003 2010 Mystic Fractal ar Fractal Zplot Application Help 5 7 1 9 5 7 1 10 5 7 1 11 5 7 1 12 5 7 1 13 5 7 1 14 5 7 2 Log High Log High Maps hill or mountain type plots with a logarithmic slope based on iterations esc
38. t5 fn fn z c user defined complex set When the first function is 742 and the second function is conj z this becomes the z conjugate set zz2 c the tricorn set Note 12 t6 Volterra Lotka equations discretized by modified Huen method from The Beauty of Fractals t7 c z c tetration of z t8 q 2 c Quaternion set from Computer Pattern Chaos and Beauty Note 8 t9 z cz 1 try with Newton s method applied A buggy algorithm found this one u0 Mandelbulb sine based non trig version Note21 ul Mandelbulb cosine based non trig version u2 Mandelbulb sine based trig version u3 Mandelbulb cosine based trig version u4 Tricorn Mandelbulb sine based non trig version Note 22 u5 Tricorn Mandelbulb cosine based non trig version u6 Tricorn Mandelbulb sine based trig version u7 Tricorn Mandelbulb cosine based trig version FraSZle QuaSZ formulas a0 spiral network C Pickover al zez 3 cec a2 tan z z 2 c a3 z 2xarcsinz c a4 cos z csc z c a5 cos z 3 c a6 z T c a7 sin z c43 a8 z 3 znec a9 Quaternion set q 34c 3 bO 1 z 2 exp z c bl 1 z 3 logz c b2 z 3 j kzn b3 cz 2 zn c 2003 2010 Mystic Fractal Fractal Zplot Application Help b4 b5 b6 b7 b8 b9 c0 cl c2 c3 c4 c5 c6 c7 c8 c9 d0 dl d2 d3 d4 d5 d6 d7
39. the extended set box to enable the extended rule set Most input files made for LParser will work with the extended set enabled but the extended rules may not work if the command is overridden by a production rule Continue Draw Continue Draw Continues a plot that was aborted early The plot is restarted at the beginning of the last row drawn Continue is disabled when an Image Merge option is selected Full Screen Full Screen Image menu Displays the entire plot expanding or shrinking the image to fit ina maximized window without title bar scroll bars or menu bar At all other times part of the picture is hidden by the inclusion of the title bar toolbar scroll bars and menu bar To exit full screen mode press any key or click the left 2003 2010 Mystic Fractal Fine Tuning menu s mouse button 5 14 Mandelbrot Mandelbrot Mandelbrots base their mapping on varying inputs of complex C which corresponds to the min max values set in the Parameters window With Mandelbrot0 Cr and Ci represent the initial value of Z before the first iteration This is normally zero but can be changed to produce non symmetrical Mandelbrots or Mandelbrots based on formulas whose initial value of Z must be non zero to generate anything such as the trig based Mandelbulb formulas Mandelbrot set 5 15 Julia Julia Julia sets normally have a fixed complex C with varying inputs of Z which corresponds to the min max values s
40. to reveal hidden detail The Mandelbulb formulas use only one type of 3D algebra based on trigonometric functions so the other Types such as quaternion are N A To produce the 3D version of Mandelbulb select Quaternion Hypernion or Complexified from the Type menu Note 22 These formulas are based on the Mandelbulb formulas using negative exponents However the coding was modified to produce a variation that closely resembles the Tricorn formula z 2 c where the imaginary part of z is multiplied by 1 The Tricorn formula is also known as the three corner hat formula The exponent is limited to the integral range 2 8 in the non trig formulas The trig based formulas support positive non integral exponents only Enter the exponent in the s box Lsystem info Lsystem info Fractal ViZion contains an extended version of the OL system string rewriting described in The Science of Fractal Images edited by Pietgen and Saupe The basic algorithm has been expanded 2003 2010 Mystic Fractal Help menu 88 and modified extensively and now supports the 3 D syntax of Laurens Lapre s LParser In addition an expanded set of rules that allow looping and 3D formula mapping lissajous curves have been added To enable the program to run at higher depth levels without extra megabytes of memory an alternate method of string interpretation has been implemented using recursion String size is kept to a minimum while the axiom is interpreted
41. user defined quad types and Fractal Projector a Fractal ViZion like version of DMZ SE limited to 3X3 matrices May 2003 QuaSZ 3 052 added genetic style function type and increased built in formulas to 180 Other additions since July 2001 generalized coloring support for external coloring and formula libraries and Thomas Kroner s loxodromic functions May 2003 FraSZle and Fractal Zplot 3 052 added random 3D orbital fractals new 3D export methods upgraded most frequently used dialogs to non modal type and added genetic style function type FZ now based on FraSZle except for built in formula list and Newton support O 2003 2010 Mystic Fractal button channel Q2 10 n dex button channel qt 11 button channel SB 9 button color 6 3 button draw 7 button formula 8 button fv 6 button help 8 button jpg 13 button load 13 button new 6 button png 13 button randrend 12 button rend 7 3d continuous potential high 41 3d continuous potential low 41 3d log high 41 3d log low 41 3d ray trace 41 3d use sea level 41 B m button save 13 button scan 7 break bioconvergence 44 button size 6 break biomorph 43 button undo 6 break biomorph off 44 button V 14 break convergence 45 button vew 7 break decomposition 47 button Light 8 break decomposition off 48 break default function 45 C break newton 44 F break orbit traps 55 break renormalization 44 Color DUS CAT OOX an
42. you to specify the name and location of the file you re about to save File Name Type a new filename to save a drawing with a different name Fractal ViZion adds the extension Zp Drives Select the drive in which you want to store the drawing Directories Select the directory in which you want to store the drawing Network Choose this button to connect to a network location assigning it a new drive letter File Load Palettes command Load Palettes command File menu Use this command to load a palette file pl The palette file contains 21 palettes created previously with Fractal ViZion or another version of the program File Save Palettes command Save Palettes command File menu Use this command to save all palettes for the current session in a palette file pl File Load Palette MAP command Load Palette MAP command File menu Use this command to load a Fractint type map file The palette in the map file replaces the currently selected palette 2003 2010 Mystic Fractal File menu o 3 9 File Load Text VZT command Load Text VZT command Load text platform independent data file Useful for transferring data files between Fractal ViZion and iViZionaire 3 10 File Save Text VZT command Save Text VZT command Save data in text platform independent format Useful for transferring data files between Fractal ViZion and iViZionaire This command is disabled for images that use the landscape
43. 150 lt Fractal Vizion Copyright c 1998 2010 by Terry W Gintz Fractal Zplot Application Help O 2003 2010 Mystic Fractal Fractal Zplot Application Help Table of Contents Foreword 0 1 Main Index 1 We A NN 1 2 Scroll bars eii IIT DIL IRIEI MIT err el EDENDI ede ere Bere 2 cpi 2 A D CT E LEE 2 5 Minimize Command oreet ad 2 6 Maximize Command ee m 3 T Dcus ii 3 8 PreviOUS WIMGOW ooccomnccconnncnnnncnnncncnnnrnnnnr E ae R nn A A E T 3 UCI ue 3 LAA R R 4 11 SWATCH OT 4 2 Fractal ViZion Remote 5 T Channel Guide ssa ener idas Naaa 5 2 New DUTLOMN aent acia 6 3 Undo button E A E A eite eere 6 ATSIZO unl REN 6 Laer 6 6 Batch button nne ti ia Ia 6 AS A ERE 6 8 Draw button secede acces sted secedi cectesdecesnedesculcasaccasencdzectenstegenscdtzcccendccgassecsscceseveegastedszcceesses 7 A ence tacndseceeudec eas Sas sceseadecaatiensdecseuseenasciasdcesuetas 7 10 Scan vtero M 7 11 Rend button ru inerenti enini ac exeveateceutebesechcabecens 7 12 View DUT D EE ia 7 13 Help DUHOM ii iii 8 E A TETTA ETT T 8 UM arcs iir E E a A E E E E E E 8 16 Light button iia 8 17 Channel I a faceted th See ec raaa A ie cts 8 18 Channe E EA iaa 9 EM A 9 20 Ch nj l SB
44. 3 abs w 14 sqrt w 15 w 16 conj w 17 csc w 18 csch w 19 sec w 20 sech w 21 cot w 22 coth w 23 cw 24 1 25 arsin w 26 arcsinh w 27 arccos w 28 arccosh w 29 arctan w 30 arctanh w 31 arccot w 32 arccoth w 33 vers w 34 covers w 35 L w 3rd degree Laguerre polynomial 36 gamma w first order gamma function 37 G w Gaussian probability function 1 sqr 2pi e 5w 2 38 c s si 39 zero 40 w s si 41 I wx l l wy l i abs 42 wy wx 1 flip 43 conj cos w cosxx 44 theta w polar angle w 45 real w 46 imag w When only fun 1 or fun 2 is used and a single user defined function is involved the function is taken from fl When two user defined functions appear in a function the f2 gadget supplies the second 2003 2010 Mystic Fractal es Fractal Zplot Application Help function type except as noted below For Newton Halley maps involving Z z the first derivative is defined as zAz 1 In z An alternate derivative formula z z z 1 is used when a non integral value is entered as an arg limit e g 0 1 This produces interesting effects though mathematically inaccurate For plots that use both fun 1 and fun 2 type 2 or 3 etc fun l takes its functions from fl and f2 and fun 2 takes its functions from f3 and f4 Note 8 The quaternion and hypercomplex functions use the complex c gadgets to input cr ci cj and ck These may be ze
45. 5 alternates between the two functions while iterating Type 6 takes the quotient of both functions Type 7 uses the lowest iterative results of both Funt1 and Fun 2 Type 8 uses the highest iterative results of both Fun l and Fun 2 Type 9 uses the Formula box to enter up to 1000 characters per formula Text can be pasted from the clipboard to the formula box by using the keystrokes shift insert Text may be moved from box to box by using shift delete to move it first to the clipboard Type 10 produces Escher like tilings for Julia sets as described in The Science of Fractal Images This uses both fun 1 and fun 2 in combination Fun sets the stage for the target set fun 2 To reproduce the images in The Science of Fractal Images use z z z for fun l and pO for fun 2 Fun may be any formula other than z z z but may produce unsymmetrical tilings Fun 2 can be any built in formula This type is mainly applicable to Julia type sets but may be used with limited effect with the MandelbrotP type set Use the Rise box in the Parameters window to set the degree of tiling desired The higher the Rise number 1 235 the greater the density of the tiling Note for quaternion Escher fractals the Rise number has no effect and Fun 1 is processed without hypercomplex extensions This results in a 3D tiling effect on the x y axis that can be multiplied by increasing the number of terms in Fun 1 as in z z z z Type 11 uses Fun 1 to produce genetic s
46. 6 2 Z Imag Z Imag Map based on the imaginary part of the complex number Z O 2003 2010 Mystic Fractal Fine Tuning menu so 5 8 16 3 Abs Z Real Abs Z Real Map based on the absolute value of the real part of the complex number Z used to map exponential Julia sets etc 5 8 16 4 Abs Z Imag Abs Z Imag Map based on the absolute value of the imaginary part of the complex number Z 5 8 16 5 Z Real Z Imag Z Real Z Imag Map based on the sum of the real part and the imaginary part of the complex number Z Changes the way banding appears in complex mappings 2003 2010 Mystic Fractal 51 Fractal Zplot Application Help 5 8 16 6 5 8 16 7 5 8 16 8 Abs Z Real Abs Z Imag Abs Z Real Abs Z Imag Map based on the absolute value of the real part plus the absolute value of the imaginary part of the complex number Z Changes the way banding appears in complex mappings Abs Z Real or Abs Z Imag gt Abs Z Real or Abs Z Imag Map based on the greater of the absolute value of the real part or the imaginary part of the complex number Z Works like a logical or where either part of z must exceed zlimit to break the iteration loop Changes the way banding appears in complex mappings Abs Z Real or Abs Z Imag Abs Z Real or Abs Z Imag Map based on the lesser of the absolute value of the real part or the imaginary part of the complex number Z Works like a logical and where bot
47. CR NE e T VUE ii 29 Ray Tracing WindOW eccceceeeeeeeeeee Ere AREENA EETAS AEE hine nn nhan nni niae sein sae nnn nnne nnn nnn 29 Octonion Values WindOW eceeeeeen enne nnnm nena uuu una n uaa asa Is 4 RR RA SR AR SR RR ARRAS ARR R4 SR SR aad 30 Edit Palette aita ree dantewa ii 30 REVES DUNA D 31 Neg Button Map Button H R Button Spread E 32 COpy A fuil MEP O E E E E T T 32 SRG Button ETA EEE A ETEA EAE E AEE EEN AA EE E AEAEE ERE 32 SRB Button fas le ciao Reset Button Cancel Button Red Slider Red edit box Green T Mee EE GreemedibDOX ONO 33 Blue Slider Blue edit box Smooth Button Scrambl a A A A A T oP A E EE ES E E ES EEA E 33 RGB Thresholds cocci apane raaa ap emaa epa aa aen aaeoa np apea eaaa Dna AEn nra a CENE 34 Edit Text command iii ia ia 34 di ALIIS L ESES E E EEE EE ES SEE ES A E bd E E E ES E EES 34 Fine Tuning menu 35 Auto Alert COMMANG ninia Ear AEAEE F 36 2003 2010 Mystic Fractal Contents Auto Time command aieiai rensa aie rii 36 Auto Rand Mii a li ia ii 37 Ree draw COMMANG iio 37 Auto Clear command 2 cccecceeee cece ence eee ee ee ence ee eee ence en enne E T A E 37 Auto Remote command 22 cccceceeeeeceee cece ee ee ee ee eee ence ee eeae enne nnnm ee seeeeeeeaa nnn
48. Formulas enter the following prefix into the Function 1 or Function 2 edit boxes a0 spiral network C Pickover al z 1 z c try with renormalization applied Sequel to t9 a2 fn z fn z c generalized form of al a3 alternate Newton Halley map of sinz c see t3 variant a4 user defined complex set fn z fn z c a5 hypercomplex Newton Halley map of h 3 c a6 Hypercomplex Newton Halley map of fn h c a7 user defined complex set fn z fn c a8 fin z zn c from Fractal Creations a9 q 34c cubic Quaternion set bO alternate Newton Halley map of exp z c as for t3 variant b1 alternate Newton Halley map of log z c b2 Newton Halley map of phoenix curve b3 cfn z zn user defined complex formula b4 fMm z kzn generalized phoenix curve formula b5 fn z a preformula for use with type 3 composite fractals uses limit gadget to select function b6 Newton Halley map of fn z fn z c b7 Newton Halley map of cfn z b8 fn z fn z c b9 Newton Halley map of foggy coastline 1 c0 Newton Halley map of foggy coastline 2 cl Newton Halley map of fn fn z c c2 cfn z where fn z first derivative of user defined function c3 fn z fn z c c4 fn z fn c c5 fn fn z c6 first order gamma function Z e z sqr 2 pi z 4c c7 Newton Halley map of fifth degree Legendre polynomial 1 8 632 5 707 34 15z dis
49. Higher scale factors make the image noisier on the respective axis x y and z The Surface Warp variable allows you to apply the same noise to a quaternion figure s shape also like a surface filter Small values are best for creating realistic surface variations like stone and wood grain 2003 2010 Mystic Fractal Fine Tuning menu s 5 9 8 Reset Noise Seed Reset Noise Seed The random noise generator is re seeded Use this to create variations on the noise texture 5 9 9 Coloring Filter Coloring Filter Here you define an hsv filter based on a real function A generalization of Earl Hinrichs sine wave coloring method the function can be any formula up to 80 characters that uses the z components x and y X and y are the real and imaginary parts of the last z value in the iteration loop Sample function sin x y cos x x The Magnify slider is used to control the intensity of the filter in conjunction with the Magnify variable in the HSV filter window Use the Preview button to see what the filter looks like with x and y ranges of 2pi to 2pi Note the coloring filter can also be used with quaternions ray traced orbital fractals and 3D height fields when the Ray Trace option is selected to map palette indexes or spreads to the x y ranges of these fractal types The variable Z is equated to the zbuffer value in this case so may also be included in the formula Quaternions and ray traced fractals normally use palet
50. OC A A A T E E A E 66 Solid GUESSING ica a 66 Window menu 67 CACAO uti a theca ick A a AAA a TT 67 MO a PEE E ia id 67 DuC Ap rec 67 Size De SK TO py oasis cise a id ai 67 2003 2010 Mystic Fractal Contents A O 67 8 Help menu 68 1 Getting Started cin 68 Qe WINGO E A O O O 69 3 HOt Keys iii 69 A O 71 5 Built in Formulas cito e iia 73 6 ES CDI o a A E aS 87 P BIDMOGKa PAY ii a 92 8 Open Avi Streami coi lolas tachan 93 QO Write Frames E cnacecesneddcasescnaecensiacdestenseecesteddeeecoovsccenstecdeeicnecccessedsencensseccans 94 10 Close Avi Stream ATAT TTT EA TT 94 Ti View AVi A TA 94 12 Batch Mode a aT a a is iii 94 13 Abo t Fractal VIZION gt ii 96 AA O A T E 97 Index 100 2003 2010 Mystic Fractal 1 1 1 Fractal Zplot Application Help Main Index Fractal ViZion User Manual Getting Started Fractal ViZion Remote Channel Guide Command menus File menu Edit menu Fine Tuning View menu Window menu Help menu Title Bar Title Bar The title bar is located along the top of a window It contains the name of the application and drawing To move the window drag the title bar Note You can also move dialog boxes by dragging their title bars A title bar may contain the following elements Application Control menu button Drawing Control menu button Maximize butto
51. Pietgen and Richter for appropriate formulas to use Basically the default mapping algorithm checks orbits for convergence to 1 or infinity and scales these points in different colors This flag is 2003 2010 Mystic Fractal 45 Fractal Zplot Application Help 5 8 8 5 8 9 mutually exclusive with the Newton Convergence and Boundary Scan flags The default method of display actually only checks if z passes through 1 This is similar to the epsilon cross mapping method For the original renormalization formulas there is a strong orbital attraction to 1 For other functions this mapping produces unusual effects with obscure mathematical foundations For the built in functions the convergence tests type 2 or 3 and 6 8 display types are the same as the ones used with the Newton flag So either method produces similar results with the same formula The differences are worth playing with though Original picture With renormalization Convergence Convergence With the Convergence flag set the program does a convergence periodic check on all points This is similar to the convergence checks done with Newton and Renormalization but also the orbits of each point are saved to determine if the orbit repeats When an orbit repeats the iteration loop is broken and the point colored according to its break time Depending on the iteration limit the last 200 points of each orbit are tracked for this check This flag is mutually
52. With this command enabled on by default the time that an image takes to plot is displayed when the plot is complete Fractal ViZion saves the condition of this option at session s end so if you disable it and close the program the option will be disabled when you restart Fractal ViZion Auto Random When this option is selected default on for every new fractal created using the New button on the Remote or on opening the program the fractal type is randomized Deselect this option if you want to select your own fractal type Redraw command Auto Redraw command Fine Tuning menu With this command disabled on by default redraw does not occur except when the Draw command is executed or Continue Most of the time you want to see the results of changing a parameter or mapping option so redraw occurs automatically with parameter or mapping changes Sometimes you want to change more than one parameter before redrawing the image or you may want to continue a mid point displacement plot after loading the file this is the only way to recreate the plot So you need to turn this option off then Auto Clear command Auto Clear command Fine Tuning menu With this command enabled on by default the drawing area is cleared before starting a new plot You can turn off this option when you want to see the effect of minor changes to parameters as they affect the plot pixel by pixel or when setting up a multiple layered fractal as ina 3D l
53. a c 9 21 Chamel Qt c is 9 2003 2010 Mystic Fractal Contents PPARCIEUNRIIMBeUMp 10 pe A TE OT 10 24 gt Channel G2 eria EE 10 25 Channel AAA A E TN 10 26 Channel Othe ARA O OT 11 A E E E E A E E E 11 28 Channel Oi 11 LI Channel HR mee IER 11 30 Channeb ED ii as 11 ST Channel AS O O 12 32 E AAA A 12 339 Channel NT iii id 12 34 Channel HY 0 a ic 12 35 Channel A m 12 36 Random Render button cccceececeeeeeeeee cece ee ee ee ence eee ee ee eee seca nien nnne nh nh nsn nah nn nnn nnns nnn nnns 12 37 Save DUMOM ERE EEIL H am 13 38 Load DUO ii a 13 39 ETC DN auiii M 13 40 Prg radio buton id 13 41 Jpg TI 13 PANE AAA A A O 13 c legem 14 GA J eiie iii dre 14 RA A eimi III MIS Mie DIIS e EP cios IRE I fens 14 3 File menu 15 1 File NeW COMMANG id 15 2 File El oegi iasi knnen raaa aa A ATEAN EDAEN ATEA ANATA NA EEA 15 File Openidialog Dox AAA ie nii a TEAs ER ls eui 16 3 File Close command coincida iia 16 4 File S ve CAM MAA ia 16 5 File Save As COMMANG ea aa rea aeaa aaa aaa aeaa ATAA aaa aaa Aaaa Aa eaaa spaa aianei 17 Fle Save as dialog DOX di 17 6 File Load Palettes command occooncconnccconncconncconncennnnnnnnnnnnnnrnnnnnnnnnrrnnnrrnnnrrnnnnrrnnrrnnanernnarrnnnes 17 7 File Save Pal
54. adjusted so that the starting line is nearly invisible with as smallest a section shown as possible to minimize odd color changes at the start of the plot For some views it is impossible to avoid a clipped polygon effect if the potential are high at the start of the function s min max zones You need to zoom out somewhat to retain the 2D image area in full screen 3D Also a horizon is established on all 3D plots at approximately 1 3 down from the top of the plot This works by clipping all points above the horizon but retaining the height of all points at or below the horizon The Y Offset controls centering of the plot up and down The plot is automatically centered left to right Use a small positive or negative offset to start under 0 5 or zero then go from there A positive y offset moves the plot down on the screen This value will change with the size of the plot or with increases in magnification Also less Y Offset is generally required on Low plots than High plots The slope factor is used to determine how steep points near the upper limit of escape times appear on screen Start with a value from 1 to 2 with Log Plots A lower limit of 1 0 is imposed for the smoothing factor Continuous potential plots usually use a slope value of 2 0 A higher O 2003 2010 Mystic Fractal Edit menu magnification factor is necessary to bring out detail on close ups Since the magnification needed for extreme close ups increases exponen
55. and the previous key frame The first key frame is written when you open a stream The next key frame is created each time you use this option In between you can zoom or change Avi variables as much as necessary The stream is only written to when this option is used The last key frame is automatically saved after the tween series is written The number of frames may range from 1 1500 frames between keys With a frame number of 1 only the key frames are written This allows animation to be created that incorporates all scalable variables in Fractal ViZion Use the Cancel button to exit this dialog without initializing a new series of frames Check the Log Scaling box if you want the frames to be written with logarithmic space between frames else linear space is used Useful when zooming where frames would otherwise be packed together at the end of the frame series Notes key frames are saved in parameter files zp with filenames of bvf_image _title zp where is the number of the keyframe and title is the name of the working fractal file 8 10 Close Avi Stream Close Avi Stream Closes any open avi stream file You need to do this before viewing the file or creating a new avi file The stream is also closed when you exit Fractal ViZion 8 11 View Avi View Avi Opens an avi file for viewing You can preview any multimedia file by clicking on its file name A multimedia box will appear to the right of the file list Click on oka
56. andscape You can use the shift c command hot keys to clear the drawing area at any time Auto Remote command Auto Remote command Fine Tuning menu With this command enabled on by default the remote is opened immediately at program startup Handy if you find the remote useful and don t want to click on the toolbar button each time the program starts up Color menu Color menu commands The Color menu offers the following commands Color Scaling menu Palette menu Divide By One Palette No split palette Divide By Two Palette Split palette into two sections Divide By Four Palette Split palette into four sections 2003 2010 Mystic Fractal Fine Tuning menu 3 Divide By Eight Palette Split palette into eight sections 5 7 1 Color Scaling menu Color Scaling menu commands The Color Scaling menu in Color menu offers the following commands Escape gt Escape time color scaling Level Color scaling based on log z Continuous Potential Color scaling based on continuous potential Use Level Use level curve option for all coloring Background Set external points to background color Set Only Plot points in complex set only Graded Palette gt Use non repeating vs modulus palette Use Palette 1 Use palette 1 for background filter Log High Logarithmic mapping of level potential Log Low Logarithmic mapping of reversed potential Continuous Potential High Linear mapping of level potential Continuous Potential
57. ape time of Z Logarithmic slopes smooth out fast changes in point potentials User specifies the level of the set point with the Rise box 0 to colors 1 Log Low Log Low Maps valley or lake type plots with a logarithmic slope based on iterations escape time of Z Logarithmic slopes smooth out fast changes in point potentials User specifies the level of the set point with the Rise box 0 to colors 1 Continuous Potential High Continuous Potential High Maps hill or mountain type plots with a logarithmic slope based on potential the absolute value of Z when the point escapes This option usually produces smoother contours with the Mandelbrot set than the Log options User specifies the level of the set point with the Rise box 0 colors 1 Continuous Potential Low Continuous Potential Low Maps valley or lake type plots with a logarithmic slope based on potential the absolute value of Z when the point escapes This option usually produces smoother contours with the Mandelbrot set than the Log options User specifies the level of the set point with the Rise box 0 colors 1 Ray Trace Ray Trace Add a light source with Phong highlights to 3d plots Color palettes should be continuous dark to light to dark to take best advantage of this option The light source parameters may be altered in the Edit Quaternion window Starting with version 1 22 this option is the default for all 3D fractal types New if you
58. around the origin to map a point s orbits This produces ring like structures The Four Circles method Paul Carlson uses four circular areas to map a point s orbit This produces sphere like structures The Square method uses an area formed by two squares around the origin to map a point s orbits This produces ring like structures with right angles The Petal method Paul Carlson also uses four trap areas to form flower like patterns Epsilon2 is used to create windows into the stalks The default value is 0 0 which produces solid stalks A window is opened to enter a value for Epsilon and Epsilon2 which are used to define the size of the trap areas 001 2 0 and 0 0 epsilon The exclude box is used to exclude the first iterations 0 99 from orbit trapping To produce the maximum 3 D effects as Phil Pickard and Paul Carlson do with these options Level Curve 4 must be set and the Cutoff value in the Parameters window should equal the negation of the epsilon value epsilon You ll need to set up a special palette with a number of color ranges that matches the split palette number if set Built in examples d3 d6 illustrate how to set up 3d like fractals To automate the process of producing Paul Carlson s 3 D like fractals a check box has been added to this window for Carlson extensions This sets the Background and Set Only flags as well as the Level Curve 4 and the cutoff value and sets the Map to lt Abs Z Real or Abs Z
59. at rectangle Otherwise the rectangle is broken into four parts and the above procedure is repeated for each part If any of the perimeter pixels are different at this pomt all the remaining pixels in the smaller rectangle are computed The screen is updated in groups of 16 lines This method can be much faster than the default single pass mode that Fractal ViZion starts in This is especially true for plots that have large areas of a single color For very intricate plots that have little open space the solid guessing mode can still be 15 20 faster The solid guessing mode can fail for some plots that have small areas of one color that are islands inside the rectangular areas under test Solid guessing is not available for Isystems orbital fractals 3D height fields or midpoint displacement 2003 2010 Mystic Fractal Fractal Zplot Application Help 7 7 1 7 2 7 3 7 4 7 5 Window menu Window menu commands The Window menu offers the following commands which enable you to arrange multiple images in the application window Cascade Arranges windows in an overlapped fashion Tile Arranges windows in non overlapped tiles Arrange Icons Arranges icons of closed windows Size Desktop Size drawing area to window frame Window 1 2 Goes to specified window Cascade Cascade command Window menu Use this command to arrange multiple opened windows in an overlapped fashion Tile Tile command Window
60. atic selection of variables options for all fractal types July 1999 Fractal Zplot 1 19 added cubic Mandelbrot support to quaternion option first pc fractal program to render true 3D Mandelbrots September 2000 Fractal Zplot 1 22 added support for full screen AVI video and extended quaternion design options October 2000 QuaSZ Quaternion System Z 1 00 stand alone quaternion hypernion cubic Mandelbrot generator November 2000 Added octonion fractals to QuaSZ 1 01 March 2001 Cubics 1 0 my first totally 3D fractal generator May 2001 QuaSZ 1 03 added Perlin noise and improved texture mapping so texture tracks with animations June 2001 Fractal Zplot 1 23 added Perlin noise and quat trap method July 2001 QuaSZ 1 05 improved performance by converting many often used dialogs to non modal type 2003 2010 Mystic Fractal 99 Fractal Zplot Application Help October 2001 FraSZle 1 0 QuaSZ formula and algebra compatible version of Fractal Zplot November 2001 DynaMaSZ 1 0 the world s first Dynamic Matrix Systems fractal generator January 2002 MiSZle 1 1 generalized fractal generator with matrix algebra extensions May 2002 DynaMaSZ SE 1 04 unreleased version scientific edition of DMZ includes support for user variable matrix dimensions 3X3 to 12X12 January 2003 Pod ME 1 0 first stand alone 3 D loxodromic generator Hydra 1 0 first 3 D generator with
61. bles to set the initial value and range of the 3rd dimension Starting from an initial value of S Si is normally set to 2 abs S when the Type is Mandelbrot Sican also be set to center the 3rd dimension on something besides 0 0 Sihas no affect in 2 D hypercomplex mode In 2 D mode the S variable acts as one of the two fixed dimensions along with the 4th Center variable The 4th Center points to the center of the fourth dimension with quaternions hypernions the 4th Dimension variable is used 2003 2010 Mystic Fractal 21 Fractal Zplot Application Help 4 6 In addition the Arg value has the following affect on cubic Mandelbrots 0 compute M using Z for z space 1 compute M using greater of S or Z for z space 2 compute M using greater of S or Z for z space 3 compute M and M use lesser of M M for pixel depth 4 compute M and M use greater of two for pixel depth 5 compute M and M use difference of two for pixel depth 6 compute M and M use sum of two for pixel depth 7 compute M and M use vector magnitude of two for pixel depth 8 compute M and M use intersection of two CCL 9 compute M and M use M or difference of two if M gt M Args 3 9 affect only cubic Mandelbrots For args 0 9 a second argument determines the plane that is used for the fourth dimension b b imag default B b real a a imag A a real A third argument also works for args
62. bsolute value of either is less than the preset zlimit the point is mapped as part of the set This method produces biological like structures in the complex plane Normally the biomorph tendrils are colored in the set color the color reserved for non divergent or inner points With the Set Only flag on the tendrils are colored according to the color scaling option used other external points are colored in the background color A window is opened each time this option is selected to set a color for the area that falls within the biomorph trap This can be 0 235 2003 2010 Mystic Fractal Fine Tuning menu 5 8 3 Bioconvergence Bioconvergence This option relates the Biomorph method to convergence for convergent type fractals Newton Renormalization and Convergence A pseudo biomorphic algorithm is applied to converging points 5 8 4 Biomorph Off Biomorph Off Turns off the biomorph flag including bioconvergence too Alternatively you can enter 1 in the Biomorph window to turn off the bio flag 5 8 5 Newton Set Newton Set The Newton flag is used to map the zeros of a particular function after the Newton transformation has been applied to the function The program doesn t make the transformation z f Z f z where stands for d dx but it does allow you to map up to 6 attractors Each time the Newton flag is set a window is opened to allow you to enter up to 6 attractors or repellers of the function This flag
63. c Quaterniondescribes the Quaternion generator s data collection window 4 7 2 Quaternion Window Quaternion Window This is the data collection window for Fractal Zplot s Quaternion generator Minx maxx miny and maxy are the spatial variables for framing the quaternion object These are usually updated automatically when you use the zoom box Min Z and Max Z define the three dimensional space that is used to map the quaternion image Normally Min Z is the negative of Max Z but Min Z can be adjusted in the positive direction to shear off the front of the quaternion object This has the effect of exposing the insides of a quaternion Constl 4 are cr ci cj and ck respectively Maxiter is the same as iterations in the Parameter s window Three rotate variables determine the 3D angle of rotation Step and Fine are pitch adjustments that bear on the quality of the plot at an expense of lengthier calculations The Bailout variable can range from 000001 to 65000 For most escape time formulas that have an attractive point at infinity the bailout is set to a value 4 or greater A larger value tends to make the figure smoother and fuller with some loss of detail When the variable is set to a value less than 2003 2010 Mystic Fractal Fractal Zplot Application Help 4 7 3 4 7 4 one then a bailout routine geared to convergent formulas such as built in formulas that use Newton s method The bailout uses Alessandro Rosa s cutoff rate
64. d The default syntax follows Laurens Lapre s LParser implementation The initial heading is 0 1 0 which will move the turtle up in the direction of the y axis when no rotation is applied to the axis or a rotation of 0 0 0 All turning commands are three dimensional The following is extracted from O 2003 2010 Mystic Fractal Fractal Zplot Application Help Laurens Lapre s LParser package turm left around up vector x turn x left around up vector turn right around up vector x turn x right around up vector amp pitch down around left vector amp x pitch x down around left vector pitch up around left vector x pitch x up around left vector rollleft counter clockwise around forward vector x roll x left around forward vector rollright clockwise around forward vector gt x roll x right around forward vector turn 180 deg around up vector roll 180 deg around forward vector roll until horizontal turn pitch roll in a random direction X in a random direction with a maximum of x degrees t correction for gravity with 0 2 t x correction for gravity with x F move forward and draw full length record vertex F x move x forward and draw record vertex Z move forward and draw half length record vertex Z x move x forward and draw record vertex f move forward with full length record vertex f x move x forward record vertex z move forward with half length record
65. e button to transfer any text from the Edit Text window to the picture Can be used with Undo Use the Edit Text command to change font text color or format text into multiple lines This is useful for adding copyright author info to a finished picture Parser Parser Information Functions capital letters are optional and parenthesis are necessary around complex expressions The following information takes the form standard function form used by Fractal ViZion to represent standard function sine Z sin z or SIN Z where Z can be any complex expression hyperbolic sine z sinh z or SINH Z arcsine z asin z or ASIN Z cosine z cos z or COS Z hyperbolic cosine z cosh z or COSH Z arccosine z acos z or ACOS Z tangent z tan z or TAN Z hyperbolic tangent z tanh z or TANH Z arctangent z atan z_ or ATAN Z cotangent z cotan z or COTAN Z arccotangent z acotan z or ACOTAN Z ez exp z or EXP z the exponential function natural log of z log z or LOG Z absolute value of z abs z or ABS Z square root of z sqrt z or SQRT Z z squared sqr z or SOR Z real part of z real z or REAL Z imaginary part of z imag z or IMAG Z modulus of z mod z or MOD Z or Izl x x y y conjugate of z conj z or CONJ 2 x yi flip z flip z or FLIP Z exchange real and imaginary parts of z y x1 polar angle of z theta z
66. e linear space is used Useful when zooming where frames would otherwise be packed together at the end of the frame series 2 44 button button Closes any open avi stream file You need to do this before viewing the file or creating a new avi file The stream is also closed when you exit Fractal ViZion 2 45 V button V button Opens an avi file for viewing You can preview any multimedia file by clicking on its file name A multimedia box will appear to the right of the file list Click on okay to open the main view window There are buttons to Play a file forwards or Backwards or forward automatically with Auto rewind repeat Click on Slow to slow down a video Each click on Slow halves the viewing speed A click on Stop freezes viewing and restores the view speed to normal playback Use the Open button to view a different avi file Use the Save button to save the file in a different compression format You must use a different name to save the file than the name that was used to open it Click on the left mouse button or any key to abort a save operation Note the view avi requester can be used to preview any multimedia file including midi files 2003 2010 Mystic Fractal 15 Fractal Zplot Application Help 3 3 1 3 2 File menu File menu commands The File menu offers the following commands New Creates a new drawing Open Opens an existing drawing Close Closes an opened drawing Save Saves an ope
67. e you want to open Drives Select the drive in which Fractal ViZion stores the file that you want to open Directories Select the directory in which Fractal ViZion stores the file that you want to open Network Choose this button to connect to a network location assigning it a new drive letter 3 3 File Close command Close command File menu Use this command to close the window containing the active image If you close a window without saving you lose all changes made since the last time you saved tt You can also close a drawing by using the Close icon on the drawing window as shown below 3 4 File Save command Save command File menu Use this command to save the active drawing to its current name and directory When you save a drawing for the first time Fractal ViZion displays the Save As dialog box so you can name your drawing If you want to change the name and directory of an existing drawing before you save it choose the Save As command Shortcuts Toolbar Keys CTRL S 2003 2010 Mystic Fractal Fractal Zplot Application Help 3 5 3 5 1 3 6 3 7 3 8 File Save As command Save As command File menu Use this command to save and name the active drawing Fractal ViZion displays the Save As dialog box so you can name your drawing To save a drawing with its existing name and directory use the Save command File Save as dialog box File Save As dialog box The following options allow
68. eck to randomize decomposition option Escape default off check to randomize escape coloring methods S Arglimit default off check to randomize s variable and arglimit variable Invert default off check to randomize invert option For quaternions you have the option of selecting only quaternion types only hypernion types hypercomplex or a mixture of quaternion hypernion types For Isystems you can set the mutation mode to Fixed to allow a limited number of mutation factors This results in an lsystem that remains the same number of lines as the original un mutated Isystem The base Isystem can be chosen at random or only the current Isystem is mutated over and over Use the Edit Axiom window to set the current Isystem Each random lsystem starts with the base Isystem to keep some consistency in the O 2003 2010 Mystic Fractal 8 13 Help menu NOS mutated image You can also control the size of the Isystem small mutations can create very large Isystems which can bog down the batch mode by setting the Max Lines variable to a smaller value default is 25000 A good value to use is 5000 Up to 5000 lines of the Isystem will be drawn before moving on to the next Isystem in the batch Note the max lines variable isn t saved with the image s data file so the image can be recreated with any suitable lines limit when not in batch mode Many lsystems don t exceed 5000 lines About Fractal ViZion About Fractal ViZi
69. ed for any turning command that doesn t use an additional argument Enter an axiom up to 255 characters in the axiom box Enter the initial width of the line gt 1 Angle and width variables can be non integer A line with width greater than one causes the turtle to draw a tubular line in 3D space See the s rule Demo Lsystem info in the extended rule set for info on changing the line shape Click on Apply to apply the current axiom to the image Click on Okay to set the new axiom into memory and close the window Click on Sample or Random Sample to use one of the pre existing Isystems in the startup directory Click on Rules to edit the rules associated with the current axiom Rules Window LSystem Rules The top row contains the command line buttons and the input boxes below are used to enter production rules and labels The input boxes Rule enter up to 255 characters for each production rule Label the label for the production rule Can be any ASCII character If the character has no keyboard equivalent you can enter it as its decimal number 0 255 This may or may not produce O 2003 2010 Mystic Fractal Edit menu 28 a visible character when drawn in the rules list Using shift delete and shift insert for these characters enables them to be copied and pasted into any rule The command line buttons Add adds whatever production rule has been entered into the string gadgets ifthe label does not dup
70. ed on Paul Carlson s bubble and stalk methods Q1 Random Quaternion Hypernion traditional 3D quaternion and hypercomplex quaternion fractals Q2 Random Quaternion Hypernion 2 extended search through non traditional formulas C1 Random Cubic Mandelbrot fractals C2 Random Cubic Mandelbrot relaxed formulas parameters CJ Random Cubic Julia fractals O1 Random Octonion fractals 02 Random Octonion2 fractals extended dimensional search QT Random Quat trap fractals HF Random Julia height fields 3D rendering of Julia sets using ray tracing and continuous potential smoothing LD Random Landscapes 3D rendering using ray traced mid point displacement algorithm LS Random Lsystems 3D turtle graphics with ray traced highlights OR Random Orbital fractals 3D rendering of strange attractors O 2003 2010 Mystic Fractal Fractal ViZion Remote 6 NT Random Newton Halley Julia sets using Newton s method and Halley s methods with various convergent techniques and other rendering options HY Random Hypercomplex Julia sets using hypercomplex extensions IF Random IFS IFS slide show using techniques developed by Michael Barnsley 2 2 New button New button Use this button to create a new drawing window in Fractal ViZion 2 3 Undo button Undo button Use this command to undo the last action An image can be continued after an undo if continue was enabled before the last action but not after an ima
71. er and lighting variables are applied This allows you to see what the surface texture looks like before the fractal is finished drawing Note to randomize the coloring filter select the Random Render button View button View button Displays the entire plot expanding or shrinking the image to fit ina maximized window without title bar scroll bars or menu bar At all other times part of the picture is hidden by the inclusion of the title bar toolbar scroll bars and menu bar To exit full screen mode press any key or click the left 2003 2010 Mystic Fractal Fractal ViZion Remote e mouse button 2 13 Help button Help button Use this button to open the help index for Fractal ViZion 2 14 Pilot button Opens the Pilot window to adjust key parameters rotate zoom and redraw the figure interactively The current image is reduced to one quarter normal for faster redraw Each click on a Pilot button increments or decrements a parameter The Speed slider controls the rate at which the buttons operate default is 10 Press the space bar or Click on Ok to open a new window and draw the altered image full size Press Esc or click on Cancel to exit this mode without opening a new window Note when using this option while an AVI stream is open a new window isn t opened but the altered figure is drawn in the current draw window the changed parameters replacing the previous ones 2 15 Formula button Formula button U
72. ergence variable produce a more accurate plot while increasing the computation time somewhat On some formulas it may be necessary to reduce this variable to its smallest value 00000001 to eliminate some artifacts spots caused by non convergence at a higher limit value For the random displacement routines the S box is used to control the fractal dimension valid inputs are 0 1 0 A lower number gives the fractal a higher dimension and thus more ragged and choppy appearance In 3D mode the magnify box works as for other 3D plots except that a value of 4 1 0 is adequate for most plots For 2D plots or backgrounds the magnification factor is used as a color scalar A value less than 1 0 reduces the number of colors by the same factor This is necessary to create more realistic clouds The color palette for 2D plots is rotated by the cutoff number This allows some independent color control given the limitations of a palette based system The arg box is used to control shaping and fullness of the finished plot The plot may include random additions at every point or just the end points The shape may be scaled linearly or non linearly The following values for the arg box control random additions and shape 0 random additions at end points only linear shaping 1 random additions at every point linear shaping 2 random additions at end pomts only non linear shaping 3 random additions at every point non linear shaping About
73. ers Lsystem info Quick reference to Fractal ViZion s Isystem description and syntax About Fractal ViZion Displays the version number and author info for this application 8 1 Getting Started Welcome to Fractal ViZion wae ub This is a short tutorial that will cover some of the basic commands to make the most of Fractal ViZion For help on any menu command press shift F1 while the command is highlighted When Fractal ViZion is first started a random fractal is automatically generated There are nineteen channels of randomly generated fractals that can be accessed via Fractal ViZion s remote Use the toolbar icon to hide show the remote or Ctr R Since most fractals FV is capable of generated are configured automatically including a random palette I will touch briefly on some of the things a new user might want to explore to enhance the fractals created thus In the end the enhancements and touchups are what will give your fractals their unique personality The most basic changes to a fractal are coloring and framing Use the palette editor to modify colors on a fractal In some cases the fractal will need to be redrawn to show the color changes while other fractals that can be color cycled will show the color changes immediately You can zoom on most fractals by clicking in the draw window and using the mouse buttons to enlarge shrink the zoom box and use the left right arrow keys to rotate the zoom box Press the space bar to red
74. et h2 O C O CC O 4c octonion set h3 cO 2410 2 CC c octonion set h4 O 2 CC4O 2 C 4c octonion set h5 O 3 CC 4c octonion set h6 O 3 CC O 3 C 4c octonion set h7 O 4 CC4c octonion set h8 cO 3 CC 4c octonion set h9 O 2 CC O 3 C 4c octonion set 10 2 z c cos pi z Godwin Vickers il 2 z c sin pi z Godwin Vickers 12 2 z cit tan piz Godwin Vickers 13 1 z43 sin z c42 14 cosh Z c ztc 2 15 exp z z43 c 16 cosh Z z 2 c 2 17 1 22 2 cz C 18 tan Z czc 19 tan z 1 z 3 c42 jO cosh z cos z 1 c jl 241 243 c42 32 1 242 tan z c 33 tan z z43 c 34 1 73 cz 1 c jo Z43 tan z c j6 U z 3 tan Z c 37 tan z sin z c 38 1 242 tan z l c 39 Z4 sin z c kO Mandelbrot set sine variation kl zA1 5 c Godwin Vickers k2 z42 z4 2 s s c Escher set by Roger Bagula k3 z 2 z Iz c Roger Bagula k4 quantum set S M Ulam k5 prey predator 1 Roger Bagula k6 prey predator 2 Roger Bagula k7 Klein group 1 Roger Bagula k8 Klein group 2 Roger Bagula k9 Klein group 3 Roger Bagula O 2003 2010 Mystic Fractal Help menu 76 LO Loxodromic by Thomas Kromer fixed type L1 squared loxodrome L2 Gedatou by Thomas Kroner fixed type L3 Ventri by Thomas Kroner fixed type LA squared gedatou ES fn z cfin z Note 5 L6
75. et in the Parameters window This option without the Bound flag set generates the so called filled in Julia set which includes non escaping points as well as the Julia set Julia from Mandelbrot 2003 2010 Mystic Fractal s Fractal Zplot Application Help 5 16 5 17 Julia set Invert Invert The Invert flag inverts the plane around a circle A window is opened that allows the user to specify the circle s radius and center coordinates Select Auto Coords to let Fractal ViZion calculate the center coordinates and circle radius Using Auto Coords the new radius and center coordinates are calculated when the picture is next drawn You can zoom on an inverted picture as long as radius and center coordinates remain the same Use the Perspective box to alter the X Y symmetry of the inversion A smaller Perspective value less than 1 0 stretches the inversion in the vertical direction Original picture Inverted Invert Off Invert Off Turns off the inversion flag Alternatively you can set the inversion radius to 0 0 to turn off inversion 2003 2010 Mystic Fractal Fine Tuning menu 9 5 18 Switch Switch When a Switch flag is set you have the option of switching the real and imaginary parts of Z or switching Z for C The real part of Z is exchanged with the imaginary part of Z after each iteration Using this technique with the Mandelbrot set produces a tricorn like plot When Z is switched
76. ettes command occooncccnnccoonnccnnncconnnennnncnnnnnnnnnrnnnnrnnnnrrnnnrrnnnrrnnnnrrnnrrnnanernnrrnnnes 17 8 File Load Palette MAP command oooccoonccccnncccnncconnncnnnnnnnnncnnnnnnonnrrnnnnnnnnrrnnnnrrnnrrnnanrrnnnrnnnnes 17 9 File Load Text VZT command ooooocconncconnnccnnncconnnennnnnnnnnnonnnnnnnnnnnnnrrnnnrrennrrnnanrrnnrrnnanrrnnarrnnnes 18 10 File Save Text VZT command ooooccconnccooncnconnccconncennnenonnnonnnnnnnnrnnnnnrrnnnrnnnnrrnnnnrrnnrrnnanrrnnnrennes 18 11 Save As 7P6 X04 re iier a int 18 12 Plot to Tie iii is 18 2003 2010 Mystic Fractal m Fractal Zplot Application Help o0 BO DN a 10 11 12 13 14 15 File 1 2 3 47 5 6 COMMANO cid ia Desin 18 File Exit command cia iia dois iii 18 Edit menu 19 Edit Undo COmmMa nnd ui iii 19 Edit Copy command oi ridad 19 Edit Clip command iun erred eee AEN E EAA ANAA AENEAN POEA ALEEN PAEROA ATRE 20 Edit Paste command e iia ii lada ia 20 Cubic Valles WInOOW ic iic oec ceto dec ot caen act e n ua do C gan cec Sub dea TEE 20 Formula WindOW uri id o a ici 21 Fractal Vari bles 5 ss Parameters Window Quaternion Window Axiom Window Rules WIR OW 5 cci ec ocie cin uaa pado A A cUa via Pasa adasacnc cR Deka ex Aaa nae ua E FOR EAR ada ad dra Rao gnUa SUR a CR ERE dA REN ARR ea ERE OS DE A Or Dit FUNCION cir 2 PI Orbits Qu k Reference A beet ee el c v ERR EE E
77. f an AVI stream the program initializes a set of bmp image files Each frame is written to the directory specified in the Demo Batch mode window Each frame is numbered with a postfix to the Batch mode name from 0000 to 9999 e g quat0001 bmp There are radio boxes that allow you to customize how random variables and menu options are processed to create new fractals Formula default on check to randomize built in formula used Lighting default off check to set default lighting Symmetry default off check to randomize symmetry used Rotation default on check to randomize camera angles Coloring default off check to reset coloring parameters Iteration default off check to randomize iterations Z Space default on check to set default z space Constants default on check to randomize the complex constants cj cK Flame default off check to randomize options for the flame orbital fractal Genetic default off check to randomize genetic word strings and genes in Formula window Torus default off check to randomize torus option Orbit Trap default off check to randomize orbit traps Filters default off check to randomize filters Biomorph default off check to randomize biomorph option Converge default off check to randomize convergence options Newton Renormalization or Converge Levelcurve default off check to randomize level curves Decomposition default off ch
78. fn z fn z c L7 cfn z c L8 fn z cfn z 1 L9 fn z c m0 fn fn z c ml fn z fn c m2 fn z zn c m cfn z zn m4 fn z kzn j generalized phoenix curve m5 fn z fn z c m6 fn 1 fn z c m7 1 fn z 24c m 1 fn z 43 c m9 fn z 1 fn z c nO Sinus by Thomas Kromer fixed type nl Sinus 2 by Thomas Kromer fixed type Note 18 n2 Rings of Fire by Thomas Kromer fixed type Note 18 n3 Teres by Thomas Kromer fixed type n4 242 y c n5 2 2 y n 1 c n6 z 2 z c n7 Z22 z1 n 1 c n8 zr 2 3zi c nO zr 244ziec o0 z42 timewave n c Note 7 ol Loxodromic 2 by Thomas Kromer 02 Loxodromic 3 by Thomas Kromer 03 Sinus 4 by Thomas Kromer 04 Sinus 5 by Thomas Kromer 05 Marmor by Thomas Kromer 06 Armor by Thomas Kromer 07 Three Parameter Julia set by Kenneth Gustavsson 08 Three Parameter Julia set 2 by Kenneth Gustavsson 09 Three Parameter Cubic Julia set Kenneth Gustavsson 2003 2010 Mystic Fractal Fractal Zplot Application Help pO z 2 c the standard Mandelbrot or Julia set pl cz 1 z the self squared dragon set p2 c z 1 z alternate Mandelbrot or Julia set p3 cz 2 1 alternate Mandelbrot or Julia set p4 c42 c z 2 alternate Mandelbrot or Julia set p5 z 3 c cubic Mandelbrot or Julia set p6 z42 c 1 2z c 2 2 renormalizati
79. for C normally you get Mandelbrots from Julia sets and vice versa This option also offers an inverse to the Julia Tower with glimpses into the elusive Mandel Tower a sort of gateway to infinity 5 19 Filter Filter Based on Stephen C Ferguson s filter algorithms in his program Iterations this option allows you to choose one of 29 tail end filters to apply to any 2D plot The name of the filter corresponds roughly to its effect on the basic Mandelbrot squared set The effect will vary with the formula and fractal type chosen This overrides the Background option on the Color Scaling menu Useful to add detail to orbit trap pictures as well as perk up any otherwise ordinary picture Filters 27 29 are generalized filters that use fn4 and fn3 in the edit formula window for expanded scope The cross filters use the epsilon variable from the orbit trap window To set epsilon s value without applying an orbit trap first change the value of epsilon to the value desired and set the orbit trap flag Then turn off the orbit trap flag Epsilon value remains unchanged when the orbit trap flag is turned off The Magnify variable is used to intensify or de intensify the effect of the filter This value can range from 1 500 nominally The Add Offset box is checked when you want the filter to add an offset to the color value normally plotted The Exclude Background box works like the Add Offset box except that background pixels are unfiltered With the Re
80. formula syntax This applies if you elect to enter your own formula into one of the function boxes and use the parser to generate the plot The use of parenthesis is necessary around complex exponents or variables E g z 1 1 5e For a complete list of variables operators and functions recognized by the parser see Parser Information Up to 500 user named complex variables and constants may be included in a formula A variable must begin with a letter and may contain numbers and letters only A variable may be up to 9 characters long A constant may be up to 20 digits long including the decimal point Fractal ViZion uses syntax similar to Fractint s formula style with an initialization section followed by the main formula and an optional bailout routine Comments may be entered on the same lime with a preceding Some variables such as pixel and p1 are named after Fractint s predefined variables These are provided to allow Fractal ViZion users to more easily convert Fractint formula types to Fractal ViZion use However Fractal ViZion doesn t prompt you to enter values into p1 the cr and ci boxes or p2 the s and si boxes or p3 the limit and converge boxes Since pl is used in the iteration process as c pl cannot be used as a variable independent of c A terminates the initialization section Multiple phrases may be entered in the main formula or initialization sections on the same line by using the terminator between phrases
81. ge box and the run is halted The message box contains the characters that caused the syntax error to aid troubleshooting 8 7 Bibliography Bibliography Complex Mathematics Churchill Ruel V and Brown James Ward Complex Variables and Applications Fifth Edition McGraw Hill Publishing Company New York 1990 Korn Granino A and Korn Theresa M Manual of Mathematics McGraw Hill Publishing Company New York 1967 Fractal Theory Barnsley Michael Fractals Everywhere Academic Press Inc 1988 Devaney Robert L Chaos Fractals and Dynamics Addison Westley Publishing Company Menlo Park California 1990 Mandelbrot Benoit B The Fractal Geometry of Nature W H Freeman and Company New York 1983 2003 2010 Mystic Fractal o Fractal Zplot Application Help 8 8 Peitgen H O and Richter P H The Beauty of Fractals Springer Verlag Berlin Heidelberg 1986 Formulas and Algorithms Burington Richard Stevens Handbook of Mathematical Tables and Formulas McGraw Hill Publishng Company New York 1973 Kellison Stephen G Fundamentals of Numerical Analysis Richard D Irwin Inc Homewood Illinois 1975 Peitgen Heinz Otto and Saupe Deitmar The Science of Fractal Images Springer Verlag New York 1988 Pickover Clifford A Computers Pattern Chaos and Beauty St Martin s Press New York 1990 Stevens Roger T Fractal Programming in C M amp T Publishing
82. ge is resized Color cycling is disabled after using Undo 2 4 Size button Size button This allows you to set the drawing area for a picture independent of the Windows screen size It also shows which size is currently in use The aspect for the drawing is based on the ratio of X horizontal width to Y vertical height The custom setting allows for any size aspect that system memory will permit Videos are limited to the standard 4 3 vga aspect or 1 1 The minimum size for an image is 40X30 Note if the image is less than 100 width the aspect must be 4 3 for solid guessing to work properly 2 5 Color button Color button Use the palette editor to modify the palette s in use 2 6 Batch button Batch button Here you set parameters for batching and saving random generated images to disk 2 7 Fvr button FVR button The window opened varies with the fractal type selected and contains all the major variables that Fractal ViZion now scales between key frames of an avi stream O 2003 2010 Mystic Fractal Fractal Zplot Application Help 2 8 2 9 2 10 2 11 2 12 Draw button Draw button Use this button to draw or redraw the image for the current fractal variables Clicking inside the draw window with the left mouse button stops all plotting Use the Continue button on the toolbar to restart plotting from the current column When the Isystem option is selected a custom dialog is opened to enter Isystem draw options No
83. ghting and viewpoint variables to the built in defaults for these variables 2003 2010 Mystic Fractal Edit menu 30 4 9 Octonion Values Window Octonion Values Window Octonions built in functions HO H9 have a form of xr xit xj xk xE xI xJ xK Additional options are entered via the Arg box in the Edit Formula window Use the Randomize button to set a random value for octonion planes E K and complex constants cj cK 4 10 Edit Palette Edit Palettes Use the palette editor to modify the palette s in use It is important to realize that palettes are software simulated in Fractal ViZion since 24 bit color supports no hardware palettes so color cycling and palette switching are not fast operations as with a 256 color system that supports palettes There are copy and spread options to smooth or customize the existing palettes in Fractal ViZion You can then save all the palettes in a pl file or by saving the entire function and bitmap v1 08 saves all the palettes in the data file Colors are shown in 8 groups of 32 colors This makes it easy to create divide by 8 divide by 4 and divide by 2 palettes with 256 colors Use a start color of 0 and an end color of 255 With Fractal ViZion a palette is actually 65280 colors with each succeeding color except the last followed by 255 colors that are evenly spread from one color to the next Use the RGB slider controls to edit any color in the palette Select Copy to copy
84. h flag Newton gt Define Newton method or clear Newton flag Renormalization Renormalization Convergence Color converging points with level set colors Default Function Use default function type 2003 2010 Mystic Fractal 43 Fractal Zplot Application Help 5 8 1 5 8 2 Level Curve gt Set level curve or reset level curve flag Decomposition gt Binary or continuous decomposition Decomposition Off Reset decomposition flag Spin Increment C by scaled factor of cx at every iteration Torus Use torus method Torus Off Reset torus flag Anti Alias Anti Alias Applies a 2 to 1 or 4 to 1 averaging filter to every pixel plotted to reduce jaggies and other high frequency noise This increases the processing time 4 to 8 times so is mainly a final rendering method not for general development use Not available for most 3D type fractals for quaternions only single pass mode is supported or without ray tracing solid guessing can be used plot to file midpoint displacement 3D backgrounds or with the tesseral solid guessing method Note because of the lengthy time required for applying the anti aliasing filter and because anti aliasing calculates different smoothing colors each time the palette is changed all color cycling and palette switching hot keys are disabled with the anti alias flag set Biomorph Biomorph Biomorphs test the real Z and imaginary Z values after breaking the iteration loop Ifthe a
85. h parts of z must exceed zlimit to break the iteration loop Changes the way banding appears in complex mappings O 2003 2010 Mystic Fractal Fine Tuning menu 52 5 8 16 9 Abs Z Abs Z Map based on the absolute value of the complex number Z traditionally calculated by taking the square root of the sum of the squares of the real and imaginary parts of Z but Fractal ViZion uses only the sum modulus of z for break point tests The standard method of mapping Julia and Mandelbrot sets 5 9 3D Render menu The 3D Render menu offers the following commands Texture Scale Set scaling factor for texture Atan Coloring Use Atan algorithm for coloring Bof60 Coloring Use Bof60 algorithm for coloring Potential Coloring Color by magnitude of z Surface Filter Define surface filter Add Noise Add noise to coloring Factors Edit noise factors Reset Noise Seed Re seed random noise generator Coloring Filter Define coloring filter 5 9 1 Texture Scale Texture Scale Opens a window to edit texture scale factors The higher the scale factors the more repetitive the texture becomes You can adjust the factors to make the texture asymmetrical on the x y or z axis Scale A is used to adjust the texture scale for the atan and Bof60 coloring options 2003 2010 Mystic Fractal 53 Fractal Zplot Application Help 5 9 2 5 9 3 5 9 4 5 9 5 5 9 6 5 9 7 Atan Coloring Atan Coloring Uses an Atan algorithm by Dav
86. he application Control menu Note if you choose to exit while plotting the program does not terminate but stops the plotting so the program can be safely exited O 2003 2010 Mystic Fractal to Fractal Zplot Application Help Shortcuts Mouse Double click the application s Control menu button E x Keys ALT F4 4 Edit menu Edit menu commands The Edit menu offers the following commands Undo Undo last edit action or zoom Copy Copy the active view and put it on the Clipboard Clip Define area of view and copy to clipboard Paste Insert Clipboard contents Cubic Values Edit cubic parameters Octonion Values Edit octonion constants Quat Trap Edit quat trap parameters RGB Thresholds Set threshold values for color interpolation Text Edit and add text to drawing Preferences Startup preferences and defaults 4 1 Edit Undo command Undo command Edit menu Use this command to undo the last action An image can be continued after an undo if continue was enabled before the last action Color cycling is disabled after using Undo though Undo is disabled for bitmaps whose width is not a multiple of 8 Shortcut Keys CTRL Z 4 2 Edit Copy command Copy command Edit menu Use this command to copy the active view to the clipboard The entire view is copied to the clipboard Shortcut Keys CTRL C 2003 2010 Mystic Fractal Edit menu 4 3 Edit Clip command Clip command Edit menu
87. hecked the decomposition option is extended for extra smoothness in Fractal ViZion The number of angles is internally multiplied by 236 to track the decomposition angle more closely Consult The Beauty of Fractals by Peitgen amp Richter for a mathematical explanation of decomposition When Biomorph or Epsilon is decomposed the tendrils or hairs are decomposed as external points Use the Set Only flag to emphasize the tendrils and hairs when external decomposition is used 2003 2010 Mystic Fractal Fine Tuning menu ss Binary Decomposition Continuous External Continuous Internal 5 8 12 Decomposition Off Decomposition Off Turns off all decomposition flags and resets the Internal Eternal option to Eternal 5 8 43 Spin Spin When the Spin flag is set the complex constant is incremented by a scaled factor of cx cx c iterations at every step of iteration Unavailable for Julia Tower types 5 8 14 Torus Torus Pixels are mapped around a torus and then expanded to fit the drawing area A generalized form of Earl Hinrichs torus method variables are provided for center x and center y to define the c and z 2003 2010 Mystic Fractal so Fractal Zplot Application Help radii and may both equal 0 0 Results will vary with the formula used but resembles the warping effect found in hypercomplex images Two versions of this method are provided the Pixel method which uses pixel values to map the toru
88. id Makin to color a quaternion image Bof60 Coloring Bof60 Coloring A variation of the Bof60 algorithm found in the classic Pietgen Ricter text The Beauty of Fractals adapted by David Makin to color a quaternion image Potential Coloring Potential Coloring The magnitude of z at the quaternion border is used to color the quaternion image Surface Filter Surface Filter Here you define a quaternion surface filter based on a real function Like a colormg filter except that the formula is used to warp the quaternion s shape The Magnify variable is used to control the intensity of the filter Use the Preview button to see what the filter looks like with x and y ranges of 2pi to 2pi Use the Random Filter button to generate a random surface filter The best surface filters will use the z value and one or both of the other variables x or y Add Noise Add Noise Add noise to quaternion image texture A variation of Perlin s noise algorithm is used to add natural randomness to an image s coloring Factors Factors Edit noise factors The blend variable determines how much noise is added to an image The higher the blend the more pronounced the noise appears This also tends to darken an image which can be compensated for by decreasing Gamma The Grain variable determines the frequency of the noise The higher the grain the noisier the image appears You can adjust how the noise maps to an image by changing the scale factors
89. ithout redrawing the Isystem Click the light bulb button to redisplay a picture after changing the lighting variables or light point You enter the level of recursion into the level box The maximum level of recursion is limited to 50 Use the scale slider to set the size of the drawing 05 to 1 0 Each Isystem is pre scaled prior to drawing to approximate the size of the draw window To speed up the pre scaling the width of the line drawn isn t used to map image limits So it s possible an object may extend off the window s edges when a line width is greater than 1 and the scale is 1 In this case use a scale less than 1 to shrink fit the drawing Click on Draw to recompute and draw the current axiom Select Wire Frame to draw a wire frame model of the current axionyrules This is useful to speed up drawing while prototyping an Isystem Enter additional Steps default 1 to increase the resolution of solid rendering Each additional step increases rendering time proportionally but can increase the smoothness of certain area fills as in polygon rendering of large objects Enter a non zero mutation value to mutate the current Isystem This follows the same mutation rules as LParser Small values less than 5 can produce extremely lengthy mutations Use Fixed Mutation to limit the size of the mutated Isystem to the original size In this case the no rules are appended or inserted Only angle and movement commands are switched Select
90. le normally ranges from PI to PI so a Start value of 50 would make all angles less than 0 decrements The Z Potential filter has a range of 0 zlimit 2 for values that do not escape the iteration loop For escape values a modulus is used to bring the filter within hsv parameters For the Level Index filter and Coloring filter the Start slider represents a decrement increment of 1 to 1 The Add Offset box is checked when you want the filter to add an offset to the color value normally plotted With the Replace All box checked the filter uses only the offset for the color value which can lead to very different color rendering This differs somewhat from how the Replace All box in the Filter s windows works Here the offset is still loosely tied to the pixel s normal color With the Background Only flag checked only pixels which would normally be colored with the background color index 0 are filtered Notes The Level Index filter was designed specifically for modifying a pixel s hue though may produce interesting results applied to a pixel s saturation or value component Hsv filtering is not available with solid guessing Use the Coloring Filter window to define a coloring formula Sample coloring formula sin x x cos y y Pilot Pilot Opens the Pilot window to adjust key parameters rotate zoom and redraw the figure interactively The current image is reduced to one quarter normal for faster redraw Each click on a Pilot button increme
91. lia analog of a cubic Mandelbrot fractal is generated The essential cubic parameters are randomly adjusted to point into a four dimensional formula Like Random Julia a set of formulas GO and G1 appropriate for cubic Julias is scanned to find an interesting Julia set and then the parameters are adjusted to produce the cubic image The ranges are reset Hj is set to 2 0 and the lighting is set for optimum viewing Note This is a quasi Julia O 2003 2010 Mystic Fractal Fractal Zplot Application Help 2 26 2 27 2 28 2 29 2 30 approximation that doesn t follow traditional cubic Mandelbrot theory The quaternions produced by this method do exhibit characteristics of cubic Mandelbrots but here I am more interested in esthetics than mathematical conformity Channel O1 Random Octonion Channel O1 button A random octonion Julia fractal is generated The essential octonion parameters are randomly adjusted to point into an eight dimensional formula HO H9 and then the octonion Mandelbrot set is scanned to find an interesting area to zoom into The ranges are reset and the lighting is set for optimum viewing if lighting is checked in the Random Batch window Channel O2 Random Octonion2 Channel O2 button A random octonion Julia fractal is generated The essential octonion parameters are randomly adjusted to point into an eight dimensional formula HO H9 and then the octonion Mandelbrot set is scanned to find an inte
92. licate a label already in use Up to 255 rules can be entered The window below the string gadgets displays the current production rules in use Use the slider device to scroll through the rules if more than nineteen rules are used amp Recall are used in conjunction to edit a previously added rule Enter the number of the rule as displayed below into the box and click on Recall The rule is entered into the input boxes Alternately you may click on a displayed rule with the cursor and left mouse button and it will be recalled This enables Change and Delete to change or delete the rule An extra step here prevents changing or deleting the wrong rule by mistake Hint you can also change the rule and then Add it in the same operation if the label is changed Use Cancel to change another rule if you dont really want to change or delete the rule you Recalled box is disabled during a Recall operation Cancel cancels the recall operation Insert inserts a rule before the numbered rule as entered in the box You can insert a rule after recalling and changing it too You can t insert a rule with a label already in use You must add at least one rule before you can insert a rule Okay terminates the edit rule session and closes the edit rule window 4 7 5 Orbit Function Orbit Function Function is the edit control for entering the two letter code for one of 17 built in orbital functions A quick refere
93. loring 53 render bof60 coloring 53 render coloring filter 54 render factors 53 render filter 60 render hsv filters 60 render level curve 46 render orbit trap values 56 render potential coloring 53 render reset noise seed 54 render spin 48 render surface filler 53 render switch 60 render texture scale 52 Gu status bar 63 UT toolbar 62 type julia 58 type mandelbrot 58 V video close avi stream 94 video open avi stream 93 video view av 94 video write frames 94 2003 2010 Mystic Fractal
94. loss of colors and detail Level coloring Continuous Potential Continuous Potential A point is colored based on its continuous potential when it blows up A window is opened to set a q factor which controls the smoothness of picture color A higher q factor results in grainier pictures and excess detail Too low a q factor results in loss of colors and detail Continuous Potential coloring Use Level Curve Use Level Curve All points are colored according to the choice selected from the Level Curve Flag option Defaults to Linear Map 4 if no Level Curve is checked This works with Decomposition and other methods that would normally not use Level Curve shading O 2003 2010 Mystic Fractal Fine Tuning menu 40 5 7 1 5 Set Only Set Only The Set Only flag plots all external points in the background color 5 7 1 6 Background Background An external point is colored with the background color This works like the Set Only flag except with decomposition plots and Biomorph Epsilon plots Normally when a point is decomposed its escape time or level color is added to its arg exit angle to determine its final coloring With Background color scaling only a point s arg determines its color With Biomorph Epsilon plots all external points are colored with the background color and all Biomorph Epsilon points are colored with the set color 5 7 1 7 Graded Palette Graded Palette All points are colored with a non
95. lp 4 10 1 4 10 2 4 10 3 4 10 4 are unaffected by the Reset button Use Reverse to reverse the order of the colors in the palette This affects only those colors in the start color to end color range Useful for reversing divide by eight palettes etc for orbit trap pictures that require a reversed palette Use Neg to create a palette that is the complement of the current palette Use Smooth to create a random palette with smooth color spreads Use Scramble to create a palette with random color indexes Use SRG to switch the red and green components of all palette colors Use SRB to switch the red and blue components of all palette colors SRB and SRG are disabled in HSV mode Youcan use these buttons to form eight different palettes by repeatedly switching red green and blue components Use the Random palette button to randomize the current palette The Randomize variables rmin rmax bmin bmax gmin and gmax act as limits that are applied after the palette after initial randomizing to make the palette conform to the desired spectrum of colors Note unless you click on Reset before exiting the editor changes are permanent to the palette edited no matter which way you close the editor Okay button or close box Reverse button Reverse button Use Reverse to reverse the order of the colors in the palette This affects only those colors in the start color to end color range Useful for reversing divide by eight palettes
96. m will begin a new plot at the new coordinates You may zoom in by defining a box inside the current drawing area You zoom out by drawing a box outside the current drawing area The outer zoom limits are between 1000 and 1000 The precision is that of double precision 64 bits Note Zooming in a three dimensional plot is not supported except for quaternion plots nor is zooming on a random midpoint displacement fractal Rotating a quaternion while zooming is possible but inexact Depending on the rotational angles set in the quaternion window you may end up rotating on the z axis which may rapidly result in overshooting the area of zoom So avoid large rotations combined with high levels of zoom It is better to rotate at low zoom levels and then zoom without rotating for close ups If you change screen resolutions you must redraw the bitmap image for a function before you can accurately zoom on tt Zooming with orbital type fractals turns on magnify mode so that details of the current screen may be examined The selected area is magnified to fill the current sector or screen The x and y ranges 2003 2010 Mystic Fractal do not change though so the magnified area may not show up all at once since other areas of the function may have to be recalculated first The magnify mode can only be used on one area of a screen at a time Magnifying is then disabled until a new map is generated though the New button in the Edit Orbit Functio
97. n Minimize button Name of the application Name of the drawing Restore button O 2003 2010 Mystic Fractal Main Index 2 1 2 Scroll bars Scroll bars Displayed at the right and bottom edges of the drawing window The scroll boxes inside the scroll bars indicate your vertical and horizontal location in the drawing You can use the mouse to scroll to other parts of the drawing 1 3 Size Size command System menu Use this command to display a four headed arrow so you can size the active window with the arrow keys de After the pointer changes to the four headed arrow Press one ofthe DIRECTION keys left right up or down arrow key to move the pointer to the border you want to move 2 Press a DIRECTION key to move the border 3 Press ENTER when the window is the size you want Note This command is unavailable if you maximize the window Shortcut Mouse Drag the size bars at the corners or edges of the window 1 4 Move Move command Control menu Use this command to display a four headed arrow so you can move the active window or dialog box with the arrow keys d Note This command is unavailable if you maximize the window Shortcut Keys CTRL F7 1 5 Minimize Command Minimize command application Control menu Use this command to reduce the Fractal ViZion window to an icon 2003 2010 Mystic Fractal 3 Fractal Zplot Application Help 1 6 1 7 1 8 1 9 Shortcut
98. n u2 Mandelbulb sine based trig version u3 Mandelbulb cosine based trig version u4 Tricorn Mandelbulb sine based non trig version Note 22 u5 Tricorn Mandelbulb cosine based non trig version u6 Tricorn Mandelbulb sine based trig version u7 Tricorn Mandelbulb cosine based trig version Note 1 all pertinent menu flags must be set for built in functions to work as described Note 2 For further info on Michael Barnsley s formulas see his Fractals Everywhere Note 3 Halley map requires the Newton flag to be set This is another numerical approximation method for finding complex roots For all Newton Halley functions the Newton map is the default The Halley option is specified through the Arg Gadget the second character being set to h after the display method 1 9 E g 1hr would designate a relaxed Halley map with display method 1 Note 4 Halley and Newton maps can use one of nine display methods 1 the default mode except for functions using sinz expz logz and tanz or fn z which default to method 2 and don t use methods 1 4 or 5 colors represent the root the zero which a point 2003 2010 Mystic Fractal Help menu e converges to 2 if the Arg Gadget is set to 2 or for functions of sinz tanz logz expz and fn z colors represent the number of iterations a point takes to converge 3 if the Arg Gadget is set to 3 colors represent the number of iterations
99. n window You can increase the resolution of a magnified map though via the iterations slider Use Okay to redraw the map at increased resolution Rotating is not supported with orbital fractals 6 7 New View on Zoom command New view on zoom View menu With this option enabled a new window is opened with each zoom instead of the zoom box area replacing the original image Ignored in avi mode 6 8 Reset Reset Reset the current figure or all figures to an empty Mandelbrot All functions in the New Formula data are blanked All options on the Flags menu are reset to their default settings The Print Function Data ignores any reset figures The Ranges Only command resets only the real Z and imaginary Z ranges in the Parameters window to 2 0 and 1 5 No other menus or variables are affected This is useful in conjunction with the P command to generate and view Julia sets After setting the complex C variable via shift P Caps Lock off you need to reset the Z ranges to see the entire Julia set after zooming into a Mandelbrot set The Reset All option resets all figures 6 9 Solid Guessing Solid Guessing In the solid guessing plotting mode the program guesses at colors that lie inside rectangular areas of the plot It first computes all the perimeter pixels of a rectangle and checks if all the pixels have the same color If so all the pixels inside the rectangle are colored the same and no further calculations are done on th
100. nce to the built in formulas is found here N is the number of iterations used to produce the fractal The demo menu defaults to 1000000 for exploratory purposes Increase to its maximum value 999999999 for a smooth finished fractal Change the angle of rotation with the three rotational variables Options for the Flame type function R6 are provided as a set of check boxes Click on Apply to start a new plot or Okay to apply and close the window After the fractal is drawn you may want to try to export it as a model for other 3D graphics programs The Steps variable controls the resolution of the export model The Export Orbital command File menu only works with some orbital fractals mainly those that have a broad surface area at the center The Reset button returns all edit boxes to their original values when the window was last opened O 2003 2010 Mystic Fractal Fractal Zplot Application Help 4 7 5 1 4 8 Orbits Quick Reference Orbits Quick Reference pO Sprott strange attractor 1 pl Sprott strange attractor 2 p2 Sprott strange attractor 3 p3 Sprott strange attractor 4 p4 Sprott strange attractor 5 p5 Latoocarfian p6 Latoocarfian Mutation Alpha p7 Latoocarfian Mutation Beta p8 Latoocarfian Mutation Ceta p9 3D Attractor C Pickover r0 Lorenz 3D Attractor E Lorenz rl Million Point Sculptures C Pickover 12 Quadratic by Julian C Spro
101. ned drawing using the same file name Save As Saves an opened drawing to a specified file name Load Palettes PL Load palettes file Save Palettes PL Save palettes to file Load Palette MAP Load a Fractint map file Load Text VZT Load text platform independent data file Save Text VZT Save data in text platform independent format Save As ZP6 x64 Save in Fractal ViZion x64 format Plot To File Plot large bitmap images directly to png file Exit Exits Fractal ViZion File New command New command File menu Use this command to create a new drawing window in Fractal ViZion The image and data for the opening picture are used to create the new window You can open an existing data image file with the Open command Shortcuts Keys CTRL N File Open command Open command File menu Use this command to open an existing data image file in a new window You can open multiple image files at once Use the Window menu to switch among the multiple open images See Window 1 2 command You can create new images with the New command Shortcuts Toolbar 2003 2010 Mystic Fractal File menu 16 Keys CTRL O 3 2 1 File Open dialog box File Open dialog box The following options allow you to specify which file to open File Name Type or select the filename you want to open This box lists files with the extension you select in the List Files of Type box List Files of Type Select the type of fil
102. nts or decrements a parameter The Speed slider controls the rate at which the buttons operate default is 10 Press the space bar or Click on Ok to open a new window and draw the altered image full size Press Esc or click on Cancel to exit this mode without opening a new window Note when using this option while an AVI stream is open a new window isn t opened but the altered figure is drawn in the current draw window the changed parameters replacing the previous ones View menu View menu commands The View menu offers the following commands Toolbar Shows or hides the toolbar Status Bar Shows or hides the status bar Phoenix Phoenix Curve Cycle Cycle colors Symmetry gt Horizontal vertical or XY symmetry Zoom Zoom into rectangle New View on Zoom New view on zoom Reset gt Reset coordinates current figure or all figures 2003 2010 Mystic Fractal 6 1 View Toolbar command Toolbar command Vie w menu Use this command to display and hide the Toolbar which includes buttons for some of the most common commands in Fractal ViZion such as File Open A check mark appears next to the menu item when the Toolbar is displayed See Toolbar for help on using the toolbar 6 1 1 toolbar Toolbar Dg The toolbar is displayed across the top of the application window below the menu bar The toolbar provides quick mouse access to many tools used in Fractal ViZion To hide or display the Toolbar choose Toolbar fr
103. of the function keys any modifications to a previous palette are unaffected by the Reset button 4 10 11 Cancel Button Cancel button You can cancel a copy or spread operation with the Cancel button 4 10 12 Red Slider Red slider Use the RGB HS V slider controls to edit any color in the palette 4 10 12 1 Red edit box Red edit box Shows red hue value of selected color index O 2003 2010 Mystic Fractal 33 Fractal Zplot Application Help 4 10 13 Green Slider Green slider Use the RGB HS V slider controls to edit any color in the palette 4 10 13 1 Green edit box Green edit box Shows green saturation value of selected color index 4 10 14 Blue Slider Blue slider Use the RGB HS V slider controls to edit any color in the palette 4 10 14 1 Blue edit box Blue edit box Shows blue value magnitude of selected color index 4 10 15 Smooth Button Smooth palette button Use to create a random palette with smooth color spreads 4 10 16 Scramble Scramble Use to create a palette with random color indexes 4 11 Edit Quat trap Quat Trap Edit menu With this window you can edit and display the two separate functions that make up the quat trap fractal You can change the orbit trap width complex c or type then display the orbit trap with the Draw Trap button You can change the quaternion s function or complex c then display the quaternion with the Draw Quat button Use Apply or Okay to display the composite fractal See Orbi
104. om the View menu ALT V T Click To 3 Open the remote which contains shortcut buttons for many common tasks and options in Fractal ViZion Use Pilot to rotate zoom and adjust key parameters of 3D figures Open an existing drawing Fractal ViZion displays the Open dialog box in which you can locate and open the desired file Save the active drawing or template with a new name Fractal ViZion displays the Save As dialog box Draw Mandelbrot set Draw Julia set Zoom into rectangle Set image size Edit palette Edit formula type data Edit fractal parameters glari m ve gt N n3 v Draw image from current parameters Continue drawing Reset coordinates Bebes Show picture full screen O 2003 2010 Mystic Fractal s Fractal Zplot Application Help 6 2 6 2 1 6 3 Display info about Fractal ViZion View Status Bar Command Status Bar command View menu Use this command to display and hide the Status Bar which describes the action to be executed by the selected menu item or depressed toolbar button and keyboard latch state A check mark appears next to the menu item when the Status Bar is displayed See Status Bar for help on using the status bar status bar Status Bar The status bar is displayed at the bottom of the Fractal ViZion window To display or hide the status bar use the Status Bar command in the View menu The left area of the status bar describes actions
105. on gt gt gt gt gt Fractal ViZion v3 056 1998 2010 by Terry W Gintz Fractal ViZion graphs formulas based on 4 D complex number planes It is based on the latest version of Fractal Zplot so contains many advanced features Fractal ViZion currently supports the Mandelbrot set Julia sets and Phoenix curves with millions of mapping variations Also included are midpoint displacement routines to enhance 3D plots 3D plot types now include quaternion hypernion orbital fractals and Isystems in addition to the original height field type The complex math functions supported include sin z sinh z Z z e z z n sqrt z cos z cosh z tan z tanh z log z ln z n z and others including the gamma and Laguerre functions Up to two formulas for z using the above functions may be plotted using traditional rules for generating Mandelbrot sets Benoit B Mandelbrot and Julia sets G Julia Also there are mapping options that use non traditional methods such as the epsilon cross method Clifford A Pickover renormalization and IFS Michael Barnsley Since the formula parser is an interpreter with its inherent lack of speed 208 popular and unusual formulas have been hard coded to reduce graphing time by 40 to 60 percent plus the FraSZle formula set too Several of the built in formulas are capable of producing graphs that the program could not generate through the parser alone such as applying the Mandelbrot set to Newt
106. on A random Julia fractal is generated using Escher like tilings Type 10 in the Formula window The Rise variable in the Parameters window sets the degree of tiling 1 235 Note Sometimes it helps to reduce iterations if the tilings do not appear to be distributed throughout the circular plane 20 25 iterations is sufficient for many Escher plots Channel SB Random Stalks and Bubbles Channel S B button A random Julia fractal is generated using one of Paul Carlson s orbit traps or bubble method Channel Q1 Random Quaternion Channel Q1 button A random quaternion hypernion fractal is generated Like Random Julia a set of formulas appropriate for quaternions is scanned to find an interesting Julia set and then the parameters are adjusted to produce a quaternion or hypernion image The ranges are reset Hj is set to 2 0 and the lighting is set for optimum viewing Note for some images an hj value of 2 0 may result in a partially clipped image Sometimes it helps to increase this value to 2 5 or 3 0 but too high a value may interfere with Solid guessing 2003 2010 Mystic Fractal Fractal ViZion Remote o 2 22 Channel Q2 Random Quaternion2 Channel Q2 button A random quaternion hypernion fractal is generated Like Random Julia a set of formulas appropriate for quaternions is scanned to find an interesting Julia set and then the parameters are adjusted to produce a quaternion or hypernion image The ranges are reset
107. on formula 1 for x plane or q plane pictures Note 9 p7 z 2 j kzn Phoenix curve Ushiki Uses Fractint extensions for degree gt 2 or lt 3 p8 Julia Mandelbrot set modified from M Barnsley Note 2 p9 fn z cfn z generalized frothy basin J Alexander Note 7 q0 Qz 3 cy z2 ql 2743 c 3z42 1 q2 Newton s method applied to exp z c q3 Newton method applied to sin 2z c q4 Newton s method applied to sin3z c q5 Newton s metod applied to sinz cosz c q6 Newton s method applied to exp z sinz c q7 Newton s method applioed to exp sinz c q8 Newton s method applied to fn z c q9 Newton s method applied to fn z fn z c r0 Newton Halley map of z 3 conj z c exploratory function based on modified frothy basin rl z z z s c Biomorphs etc s may be complex using the si variable as its imaginary component r2 zs z c Biomorphs etc s may be complex using the si variable as its imaginary component r3 fn z exp z c Biomorphs etc r4 solves Newton Halley transformation of z 2 c z 1 Notes 3 4 5 11 r5 cfn z transcendental Julia curve etc r6 cexp z exponential Julia curve etc with additional plane checking when real value of Z exceeds 50 If cos imag Z gt 0 point is considered part of Julia set r7 fn z cfn z 1 generalized form of t9 r8 foggy coastline 1 Mandelbrot IFS M Barnsley Note 14 19 foggy coa
108. on s method for solving quadratic equations Also included in the built in functions are the Quaternion and hypercomplex sets of four dimensions Hypercomplex extensions as described in Fractal Creations have been incorporated into most of the Mandelbrot and Julia functions except for the Quaternion set this is itself a special 4D version of the Mandelbrot set z 2 c and the real Newton formulas and formulas f3 f9 by Sylvie Gallet Also new to Fractal ViZion are the Mandelbulb formulas by Paul Nylander and Daniel White Thanks guys for all the fish O 2003 2010 Mystic Fractal Fractal Zplot Application Help 8 13 1 Fractal ViZion requires a true color video adapter for best results Memory requirements for Fractal ViZion vary with the size of the drawing area Fractal ViZion opens on ranging from approximately 3 megabytes memory for a 640X480 area to 48 megabytes for a 2048X1536 area Special routines have been added to reduce memory requirements for large bitmaps up to 14400X10800 by writing these directly to a file instead of using a memory bitmap Acknowledgements many thanks to Paul Carlson for providing me his algorithms for 3D like fractals and allowing me to incorporate his ideas into Fractal ViZion Also special thanks to Ron Barnett for his help in setting up the animation routines to Earl Hinrichs for sharing his unique programming methods on the fractal art and programmer s lists to Frode Gill for his quaternion and
109. oop Since recursion is used to interpret a production rule character by character the can only send the interpreter back to the beginning of that loop Trying to get back to an axioms repeat loop using a from a production rule will trigger a syntax error s n number of sides in line O sides is default for a tubular line s 3 sets a wedge shaped line O 2003 2010 Mystic Fractal or Fractal Zplot Application Help while s 4 sets a cubic or square line shape Increasing the number of sides makes the line more rounded but increases draw time The sides command only works when the line width is greater than 1 A narrower line can be rounded with fewer sides to speed up drawing 3D curve lissajous commands F Ln draw segment of 3D curve centered around current position f Ln g Ln move as segment of 3D curve no drawing Z Ln draw half segment or n length segment of 3D curve Z Ln move as half segment or n length segment of 3D curve no drawing Ln rotates 3D curve s x and z heading vectors by n degrees Ln rotates 3D curve s x and z heading vectors by n degrees amp Ln rotates 3D curve s x and y heading vectors by n degrees A Ln rotates 3D curve s x and y heading vectors by n degrees lt Ln rotates 3D curve s y and z heading vectors by n degrees gt Ln rotates 3D curve s y and z heading vectors by n degrees b n set boundary limit for 3D curve
110. orbital ifs or Isystem types or the inversion or torus options to ensure a minimum of compatability between programs Some differences between rendering styles may be observed but image shapes should be maintained 3 11 Save As ZP6 x64 Save data in Fractal Zplot x64 compatible format This allows you to transfer old zp data files to a file format that can be loaded by Fractal Zplot x64 the 64 bit version of Fractal Zplot 3 12 Plot to file Plot to File Allows you to plot a large bitmap directly to a png file without the added system requirements of keeping the whole bitmap in memory The Target group sets the bitmap resolution width 800 to 14400 Drawing aspect is that of the current image Click on Okay to set the target file name and start a new plot to file Note the 3200X2400 bitmap size is suitable for 8 1 2X11 printouts at 320 720 dpi The larger bitmap sizes are suitable for poster size printouts This option is not available with the merging options or with anti aliasing Also solid guessing is disabled when using this option 3 13 File 1 2 3 4 5 6 command 1 2 3 4 5 6 command File menu Use the numbers and filenames listed at the bottom of the File menu to open the last six drawings you closed Choose the number that corresponds with the drawing you want to open 3 14 File Exit command Exit command File menu Use this command to end your Fractal ViZion session You can also use the Close command on t
111. ors that the start end colors designate Zooming is not available while plotting height fields in 3D The screen or sector is always cleared before beginning a new 2D plot but not with 3D plots or 3D backgrounds Use C to clear the screen for a new 3D plot Use B to clear a 3D background The Reset button returns all boxes and slider values to their original values when the window was opened For 3D plots there are four additional edit boxes the Magnification Factor Y Offset Slope Cutoff and Rise The Magnification Factor controls the amount of Z Axis depth for each point plotted This can range from 0 to 10000 0 Use less for smaller plots The amount of magnification used depends on the smoothing factor size of plot and iterations Excess magnification can result in a plot being clipped off the screen Note for a magnification of 0 0 the curve is totally flat and the lower boundary is clipped to the line being drawn instead of a level starting from the boundary of the plot sector In order to create full screen three dimensional plots a larger triangular plot is clipped to the sector s square limits The Size slider must be set to at least double the sectors 2D horizontal resolution for a seamless 3D rendering The 3D plot is drawn left to right so that the lower edge of the plot can be set with the Y Offset box Potential is mapped with continuous color changes from the bottom of the plot to the starting line The Y offset should be
112. ot variant g7 z 3 3s 7 2 c alternate cubic Mandelbrot variant g8 z 3 3c 2 z s cubic Mandelbrot variant g9 73 3s z c alternate cubic Mandelbrot variant h0 O C 1 C O 4c octonion set Note 4 hl cO CC 1 C O octonion set h2 O C O CC O c octonion set h3 cO 24 0 2 CC c octonion set h4 O42 CC 0 2 C c octonion set h5 O 3 CC 4c octonion set h6 O 3 CC O 3 C 4c octonion set h7 O 4 CC 4c octonion set h8 cO 3 CC 4c octonion set h9 O 2 CC 4O 3 C 4c octonion set 10 2 z c cos pi z Godwin Vickers il 2 z c sin pv z Godwin Vickers 12 2 z c tan pi z Godwin Vickers 3 1 z43 sin z c42 14 cosh z c z c2 15 exp z z43 c 16 cosh z z 2 c42 17 1 242 cz c 18 tan Z czc 19 tan zZ 1 723 c 2 j0 cosh z cos z 1 c jl 244 23 c 2 32 1 242 tan z c 33 tan z z43 c j4 Uz 3 cz l c jo z 3 tan z c 2003 2010 Mystic Fractal at Fractal Zplot Application Help j6 js j8 j9 kO kl k2 k3 k4 k5 k6 k7 k8 k9 LO L1 L2 L3 IA L5 L6 L7 L8 L9 m0 ml 1 z 3 tan Z2 c tan z sin z c 1 7 2 tan z 1 c z 4 sin Z c Mandelbrot set sine variation ZA1 5 c Godwin Vickers z 2 z 2 s y s c Escher set by Roger Bagula z 2 zl lIz c Roger Bagula quantum set S M Ulam prey
113. place All box checked the filter totally replaces the normal color value which can lead to very different color rendering With the Background Only box checked only pixels which would normally be colored with the background color index 0 are filtered 5 20 HSVFilters HSV Filters This option allows you to choose up to 3 hsv filters to apply to any 2D plot These effectively extend the range of the palette used or reassign colors independent of the limits of the palette The filters may be assigned to modify hue saturation or value component of the pixel s normal color The filters may be Iteration time based Z Potential last z Exit Angle polar based Level Index time magnitude based Coloring Filter formula magnitude based Z Potential smallest z or Orbit Trap Formula type orbit traps default to Epsilon Cross for this option The Magnify variable is used to intensify or de intensify the effect of the filter Begin with 0 5 and increase or decrease as necessary The Start slider defines the origin of the filter so that it acts as a decrement or increment for various filter values For the Iteration filter the values correspond to 0 Max Iterations Start values range 2003 2010 Mystic Fractal st Fractal Zplot Application Help 5 21 from 0 100 percent of the nominal filter range For the Iteration filter any Start value greater than 0 would make all Iterations less than the Start value decrements The Exit Ang
114. play method 2 default c8 z42 e z z 1 second order convergence formula for finding root of ze z 1 0 c9 Newton Halley map of fn z fn z c dO z s limit c anti derivative of z n s may be complex using the si variable as its imaginary component O 2003 2010 Mystic Fractal Help menu 74 dl Sterling expansion of gamma function Z e z sqr 2 pv z c d2 Newton map of fn z fn z c generalized first degree Laguerre polynomial Newton map only Note 13 d3 fn 1 fn z c d4 z 2 c where zreal abs zreal Paul Carlson s alien Julia set d5 7 2 where zreaEabs zreal cr zimag zimag ci Paul Carlson Julia set d6 cfn z c d7 Newton s method applied to x 3 y 2 cr 0 and y 3 x 2 ci 0 Newton map only from Sylvie Gallet and Fract19 par d8 Newton s method applied to fn1 x fn2 y cr 0 and fn3 fn4 ci 0 Note 15 Newton map only d9 Billl3 from Bill Rossi via the Internet e0 solves Newton Halley transformation of z j z k z 2 1 for either Julia or Mandelbrot set el solves Newton Halley transformation of z j z 2 z k for Mandelbrot and Julia set e2 solves Newton Halley transformation of z 1 z 2 z c for either Julia or Mandelbrot set e3 solves Newton Halley transformation of z j z k z 1 for either Julia or Mandelbrot set e4 Chaos Game Julia IFS M Barnsley e5 snowflake Julia IFS as described in Fractals Everywhere by M Barnsley e6
115. predator 1 Roger Bagula prey predator 2 Roger Bagula Klein group 1 Roger Bagula Klein group 2 Roger Bagula Klein group 3 Roger Bagula Loxodromic by Thomas Kromer fixed type squared loxodrome Gedatou by Thomas Kroner fixed type Ventri by Thomas Kroner fixed type squared gedatou fn z cfn z Note 5 fin z fn z c cfn z c fn z cfn z 1 fn z c fn fn Z c fn z fn c fn z zn c cfn z zn fn z kzn j generalized phoenix curve fn z fn z c fn 1 fin z c 1 fn z 2 c 1 fn z 3 e fn z 1 fn z c Sinus by Thomas Kromer fixed type Sinus 2 by Thomas Kromer fixed type Note 6 Rings of Fire by Thomas Kromer fixed type Note 6 Teres by Thomas Kromer fixed type z 2 ytc z 2 y n 1 c Z 2 Zz c O 2003 2010 Mystic Fractal Help menu amp n7 Z22 zi n 1 c n8 zr 2 3zi c n9 zr 244ziw c o0 z42 timewave n c Note 7 ol Loxodromic 2 by Thomas Kromer 02 Loxodromic 3 by Thomas Kromer 03 Sinus 4 by Thomas Kromer 04 Sinus 5 by Thomas Kromer 05 Marmor by Thomas Kromer 06 Armor by Thomas Kromer 07 Three Parameter Julia set by Kenneth Gustavsson 08 Three Parameter Julia set 2 by Kenneth Gustavsson 09 Three Parameter Cubic Julia set Kenneth Gustavsson pO z2 c Note 2 pl cz 1 z p2 z zl 2 c p3 cz 2 c p4 z42 cz42 c p5 z 34c p6 z 2 2z c 2 c p7 z 2 j kzn p8
116. prefer to generate 3D plots such as quaternions without ray tracing deselect this flag before drawing the plot The image draw will be the pre image using the existing palette as is without ray tracing Phong and shading Use Sea level Use Sea Level Imposes a water level at zero potential for 3D plots All pomts below zero potential are mapped at zero to create lakes or oceans around land areas Palette menu Palette menu commands The Palette menu in Color menu offers the following commands 2003 2010 Mystic Fractal Fine Tuning menu Palette 1 21 Use one of 21 palettes 5 7 2 4 Palette 1 21 command Palette command Palette menu Switch to palette 5 7 3 Color Divpal1 command Divide by One Palette Color menu Palette is not split before applying to pixel 5 7 4 Color Divpal2 command Divide by Two Palette Color menu Palette is split into two parts before applying to pixel 5 7 5 Color Divpal4 command Divide by Four Palette Color menu Palette is split into four parts before applying to pixel 5 7 6 Color Divpal8 command Divide by Eight Palette Color menu Palette is split into eight parts before applying to pixel 5 8 2D Render menu 2D Render menu commands The 2D Render menu offers the following commands Anti Alias Use anti aliasing with 1X4 or 1 X2 super sampling Biomorph Escape on any part of z Bioconvergence Relates Biomorph method to convergence Biomorph Off Reset biomorp
117. r the fourth dimension b b imag default B b real a a imag A a real A third argument also works for args 0 9 j alternate cubic Mandelbrot mapping for compatibility with alpha versions of Fractal Zplot 1 19 Therefore an arg value of 3B uses the union of M and M and b real as the fourth dimension Note 18 For the loxodromic functions Sinus 2 and Rings of Fire the Arg Limit variable in the Edit Formula Type window is used as an additional ingredient Try values 1 5 to 1 5 for Sinus 42 and 1 5 or PI 2 for Rings of Fire Note 19 Octonions have a form of xr xit xj xk xE xI xJ xK For these formulas C is the octonion constant 1 1 1 1 1 1 1 1 and CC is the octonion conjugate 1 1 1 1 1 1 1 1 O 2003 2010 Mystic Fractal Fractal Zplot Application Help 8 6 Additional options are entered via the Arg box in the Quaternion editor window To rotate the extra four octonion dimensions E K use the following syntax OI rotate OE OK to OI OE OJ rotate OE OK to OJ OI OK rotate OE OK to OK OJ To normalize the C and CC constants n normalize C and CC default is un normalized Alternate octonion initialization c set OE OK to 01 at beginning of each iteration With octonions you have your choice of two different algebraic systems depending on whether the Type is set to Quaternion or Hypernion Hyper octonions use alternate definitions of the basic octonion multiplication tables This
118. rE le 1 2 71828 read write i ior I square root of 1 read write iteration iter iteration loop counter j Hor JA real part of the complex constant read only k k or K coefficient of the imaginary part of the complex constant read only Note j and k are the actual values of the complex constant terms as they are used in the iteration process so will vary when the Mandelbrot option is used m m or MF or pixel a complex variable mapped to the pixel location as defined by the z coordinates entered in the Parameters window read write maxit the maximum number of iterations as set in the Parameters window read only p p or P real constant used in phoenix maps uses the real part of the complex constant when the Phoenix option is chosen read only pl the complex constant entered in the cr and ci gadgets read only pi pior PI 3 14159 read write q q amp or Q real constant used in phoenix maps uses the imaginary part of the complex constant when the Phoenix option is chosen read only X x or X real part of Z read write O 2003 2010 Mystic Fractal Fractal Zplot Application Help 8 5 y y or Y coefficient of the imaginary part of Z read write z zor Z function value at any stage of the iteration process read write zn or ZN the value of z at the previous stage of iteration read only Built in Formulas Built in
119. ractal 35 Fractal Zplot Application Help saved in the file prefs txt when you close the program if the Defaults check box is selected The check boxes in the group Save on Program Close allow you to change the default startup mode of a few Auto options such as Auto Redraw and the Random Setup variables By keeping the boxes selected Fractal ViZion saves the last changes you make to these options If you want to go back to the initial settings the way Fractal ViZion was packaged originally you can click on the Reset Defaults button This restores the data Auto variables and random setup defaults Use the Reset Dialog Positions button to reset all non modal dialog positions to x y positions that will fit within a 640X480 screen Sometimes when you switch screen resolutions to a lower resolution there might be dialogs that are off the screen and thus are inaccessible when reopened This can happen too if the Registry key for the dialog position becomes corrupt The program keeps track of all non modal dialogs last positions in the Software portion of the Registry Close all open dialog windows you want to reset before using this command or open a New draw window before using the command Use the Default Directories tab to change the default directories for saved and loaded items in Fractal ViZion Click on the button next to each default directory box and use the folder requester to pick a different directory or create a new direc
120. raw the fractal using the new zoom coordinates or click on the window s frame or title bar to abort a zoom O 2003 2010 Mystic Fractal 9 Fractal Zplot Application Help 8 2 8 3 Note zooming is not available on lsystem or landscape fractals and rotating may be disabled when some types of symmetry are used Additional changes to the fractal may be made via the FVR button on the FV remote Most fractal types have additional variables that can be varied for animation purposes or for general esthetics Some specialized filters can be applied to the fractal via the Fine Tuning menu and symmetry can be altered via the View menu This completes the Getting Started tutorial Be sure to read the hot keys palette editor and remote sections for additional info The Bibliography lists additional reference material for a better understanding of the fractal types and functions contained in Fractal ViZion Index Index command Help menu Use this command to display the opening screen of Help From the opening screen you can jump to step by step instructions for using Fractal ViZion and various types of reference information Once you open Help you can click the Contents button whenever you want to return to the opening screen Hot Keys Hot keys CtrH F1 CtrH F9 Ctr F11 Ctrb 0 Ctrb 9 change to one of 21 color palettes useable during plotting CtrH F12 holds the palette of the most recently loaded function Tab
121. re already used as the starting value of z0 6 4 Cycle command Cycle command Color menu Use this command to cycle colors when not plotting Works with any coloring mode but not with hsv filtering or anti aliasmg Undoing an action disables the cycle command until the image is redrawn 6 5 Symmetry Symmetry This produces a mirror image from left to right vertical or top to bottom horizontal or both xy You can zoom with symmetry but the results will be uncertain if the zoom box is off center on the window or if rotation is used Symmetry has no effect when used with the Tesseral option 3D or random fractals Vertical symmetry 2003 2010 Mystic Fractal 55 Fractal Zplot Application Help 6 6 Horizontal symmetry XY symmetry Zoom Zoom Turns on zoom mode so that detail of the current plot may be magnified Alternatively just click inside any drawing window move the mouse and the zoom box will appear Using the mouse move the zoom box over the portion of the plot you wish to magnify Hold the left mouse button to shrink the box or the right button to enlarge it Use the left and right arrow keys to rotate the box counter clockwise or clockwise Use the up and down arrow keys to squash or expand the box changing the aspect of the image You start a zoom by pressing the space bar You abort a zoom by clicking outside the main window or in the title bar or by pressing the escape key The progra
122. resting area to zoom into The ranges are reset and the lighting is set for optimum viewing This option uses the octonion formulas H0 H9 with random dimensional switching one of OE OK for Oi to create octonion fractals that may extend to eight dimensions Channel QT Random Quat Trap Channel QT button A random quat trap fractal is generated using one of Paul Carlson s orbit trap methods and a quaternion image A separate image is created for both quaternion and orbit trap formulas in figures 1 and 2 then the figures are merged and drawn as one image See Orbit Trap options for further details on quat trap pictures Channel HF Random 3D Julia Field Channel HF button A 3D height field fractal is generated for a random Julia set Like Random Julia a set of formulas appropriate for 3D height fields is scanned to find an interesting Julia set and then the parameters are adjusted to produce a height field image The ranges are reset and the lighting is set for optimum viewing Channel LD Random Landscape Channel LD button A random 3D landscape midpoint displacement fractal is generated O 2003 2010 Mystic Fractal Fractal ViZion Remote 12 2 31 Channel LS Random Lystem Channel LS button A random Isystem fractal is generated An ls file is selected at random from the startup directory the palette randomized and then a random amount of mutation is applied The lighting is set for optimal viewing and the figure
123. ro when generating a Mandelbrot like set of these functions Julia sets may then be mapped by grabbing points cr ci from interesting areas near this set Cj and ck must be entered manually for Julia sets The hj and hk gadgets are used to input the z and w coefficients of the j and k planes Use small amounts to start for these variables 0 1 0 Values of O for hj hk cj and ck result in a two dimensional slice that matches the standard non hypercomplex type Higher values of z and w as wellas cj and ck produce more pronounced asymmetry in the complex mapping Note 9 Renormalization functions use the Arg Gadget for plotting options 1 4 6 8 as follows 0 or 1 default renormal with anti ferromagnetic points mapped only for Julia sets Paramagnetic points those converging to 1 and ferromagnetic points those escaping to infinity are mapped for both Mandelbrot and Julia sets 2 anti ferromagnetic points are mapped for the Mandelbrot set This is actually a level set mapping for points that do not escape to infinity or converge to 1 3 uses an alternate convergence formula for paramagnetic and anti ferromagnetic points 4 a combination of methods 0 and 3 with characteristics of both methods appearing in plot 6 8 alternate convergence methods same as those used with Newton Halley maps An optional argument for renormalization n follows the convergence method This is an alternate bailout method for ferromagnetic points Note 10
124. rotated a random amount on the x y and z axis 2 32 ChannelOR Random Orbital Channel OR button A 3D orbital fractal is generated by randomizing parameters for one of nine strange attractors Based on Sprott s method of using random affine transformations to find interesting strange attractors 2 33 Channel NT Random Newton Halley Channel NT button A random Julia fractal is generated using Newton s method or one of Halley s methods 2 34 Channel HY Random Hypercomplex Channel HY button A random Julia fractal is generated with hypercomplex extensions 2 35 Channel IF IFS Slide Show Channel IF button A random slide show of ifs images is displayed in the active view The show is based on 11 different base forms that are randomized to create millions of variations Press the home key to see the base forms only Press the end key to display randomized images Press the r key to repeat the current form Press the backspace key to display all forms Press the escape key or left mouse button to end the show 2 36 Random Render button Random Render button The rendering options for the current fractal are randomized Does not affect formula or range variables For quaternion and 3D height fields a random coloring filter is applied 2003 2010 Mystic Fractal 13 Fractal Zplot Application Help 2 37 2 38 2 39 2 40 2 41 2 42 Save button Save button Use this button to save and name the active dra
125. s nnn nh nnns nnn nn nennt 37 NJ O oO BO I ers fel ol tl 381 ccoo ects TERTII CR I ICI Color Scaling menu ESCapey rcnt kie ee EM AN uA Ms to dl cM e dcin ett Ear dde dt dice e zens dees E2U MEETS Continuous Potential estote A EE ERRAT ADI UHR 39 Use Level CUNVe Es 39 OR E E ANA 40 seio 40 Graded Palette aa nte e 40 Use Paletle ure a ra 40 Log High Log Low Continuous Potential High o eta ennt rr DU Er tae 41 Continuous Potential LOW eitis re a eat 41 A e TD D O EEETERER Use Sea O E EE Palette Sul P Palette 1 21 command Color Divpali command Color Divpal2 command Color Divpal4 command Color Divpal8 command 8 2D Render Mena iii PUBL a rr M A rnm Bioconvergence BlOMOFPA Off ELE A ere Da ole AN On O i Juri jeder Default Function Level Curve Decomposition DECOM POSITION Off Y 48 SPU NEU nce eC ICI IM ne DLL OPUS Mr AAPP ne LRD ii o late iste een LAA o Abs Z Real NA O DD Z Real Z Imag Abs Z Real FADS LAMA iii a ias 51 NANA sss nennen nennen rennen enne nnne nnne nnne 51 Abs Z Real or Abs Z Imag nr rece ene Rene cede eds pe pue rotae un DR tee heen 51 O 2003 2010 Mystic Fractal Fractal Zplot Applica
126. s to the fractal space and the Two Pi method which uses an initial rectangle 2 pi by 2 pito map the torus to a fractal image With the Two Pi method when you zoom the rectangle s size and starting points are changed to match the zooming area The rectangle s coordinates are saved with the fractal If you turn off the torus flag after zooming and then reinitialize the torus flag the rectangle reverts to a 2X2 area so the image will change accordingly Rotating is not supported for the Two Pi method but does work in a limited way with the Pixel method 5 8 15 Torus Off Torus Off Turns off the torus flag Alternatively you can enter a negative value to turn off this flag 5 8 16 Map menu Map menu commands The Map menu offers the following commands Z Real Mapping based on real part of z only Z Imag Mapping based on imaginary part of z only Abs Z Real Mapping based on absolute value of real part of z Abs Z Imag Mapping based on absolute value of imaginary part of z Z Real Z Imag Mapping based on sum of parts of z Abs Z Real Abs Z Imag Mapping based on absolute value of parts of z gt Abs Z Real or Abs Z Imag Mapping based on highest absolute value of parts of z lt Abs Z Real or Abs Z Imag Mapping based on lowest absolute value of parts of z Abs Z Mapping based on absolute value of z 5 8 16 1 Z Real Z Real Map based on the real part of the complex number Z used to map exponential Julia sets etc 5 8 1
127. se this button to change formulas or type 2 16 Light button Light button Edit lightpoint and viewpoint variables 2 17 Channel J1 Random Julia Channel J1 button A random Julia fractal is generated Many of the rendering options of Fractal ViZion are selected on a random basis and the Mandelbrot space for one of the 180 built in formulas is scanned for an interesting Julia set The palette used is also randomized Note In most case the Julia search is a short one but sometimes the seek mode can seem to get stuck when the criteria for an interesting Julia set fails to match the formula used In the latter case either click the left mouse button and restart the search process or pressing a palette key will sometimes override the current search and restart it if HSV filtering has been selected Tip some things remain to be done after the Julia set is drawn The algorithm doesn t check the type of split palette that is used so a mismatch in the Divide by color option may need correcting e g Divide by four may be selected for a divide by eight palette Feel free to experiment with all the parameters reframe the image change palettes etc This routine provides a fast intro to many options in Fractal ViZion that the user may be unfamiliar with no knowledge of fractal science math required 2003 2010 Mystic Fractal 9 Fractal Zplot Application Help 2 18 2 19 2 20 2 21 Channel J2 Random Julia Chamnel J2 button
128. sk List to switch to or close an application on the list Shortcut Keys CTRL ESC Dialog Box Options When you choose the Switch To command you will be presented with a dialog box with the following options Task List Select the application you want to switch to or close Switch To Makes the selected application active End Task Closes the selected application Cancel Closes the Task List box Cascade Arranges open applications so they overlap and you can see each title bar This option does not affect applications reduced to icons Tile Arranges open applications into windows that do not overlap This option does not affect applications reduced to icons Arrange Icons Arranges the icons of all minimized applications across the bottom of the screen 2003 2010 Mystic Fractal 5 Fractal Zplot Application Help 2 2 1 Fractal ViZion Remote Fractal ViZion Remote The remote provides access to many of the most used commands in Fractal ViZion Info about each button can be obtained by using the located near the close box in the top right hand corner Channel Guide Channel Guide The nineteen channels accessed via the FV remote J1 Random Julia basic Julia sets using one formula and many different rendering options J2 Random Julia 2 includes more advanced composite type fractals using two formulas ES Random Escher like fractals Julia fractal set using Escher mapping S B Random Bubbles and Stalks bas
129. stline 2 Mandelbrot IFS M Barnsley Note 14 sO solves Newton Halley transformation of sinz c s sexpz c transcendental Mandelbrot or Julia set s2 c 1 z 2 2 z7 2 1 alternate Mandelbrot Julia set s3 solves Newton Halley transform of tan z c s4 IFS x sy j y sx k x20 else x sy j y sx k modified from M Barnsley An alternate version of this formula is executed when the limit value is non integral s5 solves Newton Halley transform of z s 1 Julia set only s6 composite function cz c z amp z 2 c C Pickover O 2003 2010 Mystic Fractal Help menu 78 s7 transcendental function fn z c s8 z 343 c 1 z c 1 c 2 3 24243 c 2 z c 2 3c 3 2 renormalization formula 2 for x plane or q plane pictures s9 Newton Halley map of z z limit 1 Julia set only t0 Newton Halley map of z Z limit c Julia or Mandelbrot set display method 2 default limit gt 1 0 use 1 0 for initial z with MandelbrotO type or use MandelbrotP type t1 Newton Halley map of Chebyshev function cos n arccos x t2 Newton Halley map of Hermite polynomial 16x 4 48x 2 12 13 alternate Newton Halley map of tanz c Julia or Mandelbrot set the twist is in the second derivative of the Halley type t4 Newton Halley map of z limit c Julia or Mandelbrot set display method 2 default limit gt 1 0 use 1 0 for initial z with MandelbrotO type or use MandelbrotP type
130. t Trap options for further details on quat trap pictures 4 12 Size Size command This allows you to set the drawing area for a picture independent of the Windows screen size It also shows which size is currently in use The aspect for the drawing is based on the ratio of X horizontal width to Y vertical height The custom setting allows for any size aspect that system 2003 2010 Mystic Fractal Edit menu 34 memory will permit Videos are limited to the standard 4 3 vga aspect or 1 1 Midi output is limited to images with the standard 4 3 aspect The minimum size for an image is 40X30 Note if the image is less than 100 width the aspect must be 4 3 for solid guessing to work properly 4 13 RGB Thresholds RGB Thresholds Edit menu When Fractal ViZion plots pixels using a simulated palette the colors are normally scaled interpolated to fit between one of 236 color indexes These 236 colors can be edited by the palette editor Sometimes you don t want an intermediate color to be plotted if adjacent color indexes differ a lot There are two tests that can be made to determine the degree of color difference between adjacent color indexes The first is RGB where the difference in individual components is tested The thresholds are set so that color indexes that differ in values exceeding the individual RGB thresholds will bypass the interpolation process The values can be set from 0 to 255 with 255 the default At 255
131. t decomposition flag Spin Increment C by scaled factor of cx at every iteration Torus Use torus method Torus Off Reset torus flag The following commands can be used via the 3D Render Menu Texture Scale Set scaling factor for texture Atan Coloring Use Atan algorithm for coloring Bof60 Coloring Use Bof60 algorithm for coloring Potential Coloring Color by magnitude of z Surface Filter Define surface filter Add Noise Add noise to coloring Factors Edit noise factors Reset Noise Seed Re seed random noise generator Coloring Filter Define coloring filter Invert Invert image around circle Invert Off Reset inversion flag Switch gt Switch z components or z for c Filter Choose an optional tail end filter HSV Filters Define HSV filters Orbit Traps Set orbit trapping method 5 1 Auto Alert command Auto Sound Alert command Fine Tuning menu With this command enabled on by default the user is notified by a sound clip when a drawing is completed or user canceled By disabling this command the completion exclamation is suppressed and also any alert that contains a message box Note some sound clips are automatically generated by Windows or there is no text alert for a given error condition In these cases the sound alert is unaffected by the Auto Alert command 5 2 Auto Time command Auto Time command Fine Tuning menu 2003 2010 Mystic Fractal Fractal Zplot Application Help 5 3 5 4 5 5 5 6 5 7
132. takes z to reach its smallest value Level curves 2 3 and 5 6 are described more fully in The Beauty of Fractals Linear Map 4 is mapped like Log Map 1 with the mapped value of the function at its final iteration applied to the color palette and produces 3D like effects with the Epsilon Cross method The Log methods use a log palette while method 4 6 use linear palettes This option can override or may be overridden by many of the options in the Color Scaling menu Decomposition doesn t use Level Curve shading unless you select the Use Level Curve option Log Map 1 Small Log 2 2003 2010 Mystic Fractal Fractal Zplot Application Help 5 8 11 Indexed Log 3 Bubble 7 uses Paul Carlson s contour mapping method to produce 3D like bubble pictures The method is very sensitive to which formula is used working best with the basic Mandelbrot set z 2 c and the like Color mapping should be set to Use Level Curve This is a trial and error method that uses two other variables to produce the final effect magnify and cutoff as entered in the Parameters window Magnify is used to screen unwanted background contours in the plot while cutoff is used to fill out the color palette Magnify should be a low value usually less than 1 to eliminate the contours that usually appear in escape type Mandelbrot Julia sets If it is too large the bubbles will be too crowded while too small a value will cause the bubbles to disappear
133. te the draw window that a plot is initialized in by clicking on an Okay or Apply button or Draw must have the focus to begin drawing With a lot of parameter or formula windows open for different draw windows it is easy to mistake one window for another So if the plot doesn t start immediately in the window that has the focus check to see that that window is actually the one you wanted to start a new plot in If it isn t click on the title bar for the window that the plot is activated in The plot should then commence Abort button Abort button Use this command to stop drawing Clicking inside a window s drawing area or close box or the program close box will also stop the drawing Note once a plot has started Fractal ViZion continues to draw the image for that window regardless of which drawing window has the input focus until done or aborted You can open and close other drawing windows without affecting the current drawing but only one drawing is active at any time Scan button Scan button This generates a Julia set or quaternion Julia set from a formula s Mandelbrot P space Random points in a formula s current Mandelbrot space are scanned for an interesting Julia set Rendering options are maintained in the current fractal Equivalent to the F hot keys Not used with Isystem landscape or orbital fractals Rend button Rend button For quaternion Isystems landscape orbital and 3D height fields the current coloring filt
134. te index one the second index zero being reserved for the background color for their predommant color with pixel intensities colors affected by the lighting variables When the coloring filter formula is defined up to 235 colors can be used the full palette to create mixed textures The trig and exponential functions translated include sine sin arc sine asn cosine cos arc cosine acs tangent tan hyperbolic tangent th hyperbolic sine sh hyperbolic cosine ch log log natural log In power pow arc tangent atn absolute value abs exponential exp and square root sqr The math functions are multiply subtract divide and add The constants are PI and E In 1 plus any floating point number up to 9 digits including the decimal point The power function x to the y power is entered in standard notation x y with optional parenthesis necessary around complex exponents or variables Note Range limits exist for arguments to these functions exp arc sine hyperbolic sine arc cosine hyperbolic cosine arc tangent and hyperbolic tangent 100 0 for the exponential 200 0 for hyperbolic functions 1 0 for the arc functions the log functions must be gt 0 and the power function x must be integral and non zero when y lt 0 and 0 0 is undefined Square root is undefined for x 0 No filtering is done when these limits are exceeded Syntax for an acceptable formula is AS XY bs
135. ternions use the S and Si variables in the New Formula window to set the initial value and range of the 3rd dimension Starting from an initial value of S Si is normally set to 2 abs S when the Type is MandelbrotP or Julia Tower Sican also be set to center the 3rd dimension on something besides 0 0 Si has no affect on MandelbrotO or Julia types height fields or in 2D mode In 2D mode the S variable acts as one of the two fixed dimensions along with the Limit variable The Limit variable NF window points to the fourth dimension in the Quaternion window the 4th Dim variable points to hk In addition the Arg value entered in NF window has the followmg affect on cubic Mandelbrots 0 compute M using hj for z space 1 compute M using greater of S or hj for z space 2 compute M using greater of S or hy for z space 3 compute M and M use lesser of M M for pixel depth 4 compute M and M use greater of two for pixel depth 5 compute M and M use difference of two for pixel depth 6 compute M and M use sum of two for pixel depth 7 compute M and M use vector magnitude of two for pixel depth 8 compute M and M use intersection of two CCL 9 compute M and M use M or difference of two if M gt M Args 3 9 affect only quaternion type cubic Mandelbrots while args 0 2 can be used in 2D mode or with height fields For args 0 9 a second argument determines the plane that is used fo
136. the horizontal resolution while the vertical resolution is then scaled according to the full screen VGA ratio 4 to 3 1 1 if that aspect is selected through the Auto menu The Sector slider controls which of 4 sectors the picture will be drawn in if the Size is less than or equal to the full screen horizontal resolution 2 Otherwise the picture is centered according to the full screen dimensions This allows you to show zooms of a particular function by using different sectors or show the affect of different plotting options Each sector is erased individually Note if you try to 2003 2010 Mystic Fractal 25 Fractal Zplot Application Help continue a plot in a different sector than you started with the plot will continue in the original sector The Thumbnail button next to the Size slider is used to set a thumbnail size quickly The thumbnail size toggles between 1 4 and 1 8 of the horizontal screen resolution e g 200X150 or 100X75 for an 800X600 screen The more iterations used the longer it takes to plot a function but more detail will be present 10 20 is sufficient for most biomorphs while more iterations will be required for Mandelbrot and Julia sets depending on the detail required Start color and end color boxes are provided to limit the palette colors that the current image uses Use start color of 0 and end color 235 to use the full palette The color cycling keys arrows and enter backspace work for only those col
137. tially with the iterations used the magnification variable also represents an exponentially increasing factor magnify log iterations For 3D height field plots the Rise box is used to specify a height for the set potential Normally the set is mapped at zero or the highest potential of colors 1 You can change this to create Mandelbrot lakes or sheer cliffs Using a Rise value of less than 0 automatically maps the set potential at the highest potential The rise value also sets the color index for the Mandelbrot lake with ray traced plots For 2D plots the Cutoff box acts as a palette multiplier or divider depending on whether the value entered is less than or greater than 1 0 The palette color is divided by the Cutoff to speed up or slow down color changes Cutoff values are limited to a low minimum of 001 For level curves and the add and multiply color scaling options use a negative cutoff value to maintain a smooth palette This ensures that the multiplier is used before the floating point palette values are converted to integer palette indexes For random displacement plots the Rise value determines the minimum height plotted Heights below the Rise value are treated as 0 altitude For 2D plots pixels at minimum height are not plotted The Rotate box is used to rotate the picture by any degree This rotates all three points that define the Z plane The rotational angle is reset to zero after each use Related Topi
138. tinuous as in the Phoenix formula Unlike the P command grabbing and drawing continues until you click on the window s frame Note when you exit the J command once you find an interesting Julia set another window is opened with the Julia type set The parameters in the original window revert to their original Mandelbrot settings Shift G like J except that a quaternion set is generated in sector 2 using an iteration count of 10 and other parameters are changed temporarily to suit quaternion plots Hj is set to 2 0 the rotational variables are reset and the light source is set to 1 1 and 3 Quaternion math is used where possible Once you find an interesting quaternion set using G like the J command another window is opened that sets the fractal parameters to those in the exploratory qjulia window fast qjulia mode The parameters in the exploratory window revert to their original Mandelbrot settings Shift W like G except this modifies the cj and ck elements of the complex constant to locate a quaternion Julia set Shift S a combination of the G and W commands The W command is implemented with the right mouse button Shift L Like G except this modifies the ci and cj elements of the complex constant to locate a quaternion Julia set This complements the loxodromic formula LO that requires a non zero cj for best results Cr should be close to zero to maintain symmetry in the loxodromic figure Shift U
139. tion Help 9 10 11 12 13 14 15 16 17 18 19 20 21 OO JO oO 5 OQ A OND a AbS Z 4 E e e RA Ed 3D Render menu Texture Scale Atan Coloring Bof60 Coloring Potential Co do 53 Surface Filter eeu tu meu cat eetes duces Oa raea aa a EEEa Aaaa EEEa 53 Add Noise Factors R set Noise AAA 54 Coloring ri GS 54 EREA nET E cis 55 Orbit trap VAlUES 56 Draw command Nec 56 Draw LSySteM COMM ANG 56 Continue Draw ciis ice A 57 FUIL SOF AAA T T E tescdascaseeatuacescasaenebscats 57 Mandelbrot AA cctv aa ae ede sedeasscceseeteerecesiecseudssecedustseaseweccesecaviceceences 58 UNA A i A danvaadeecdetets 58 MV ii 59 lius ii RE 59 SA O IN 60 clam 60 HSV Filters innu A iaa 60 Alp m anda 61 View menu 61 View Toolbar command voii ici aaa 62 E IN E A 62 View Status Bar Command ooncconncconnnccnnncnonnncnnnnnennnnnnnnrnnnnnnnnnrrnnanrrnnnrnnnnrrnnnnrrnnrrnnanrrnnarennnes 63 AUD a a 63 O AA A 63 Cycle COMMANG cenital 64 SYMIMECUY dis 64 A 65 New View on Zoom command c ececeeeeeeeee cece ee ee eee eee eeee nese ence ne seeeeeeeaeseaeeeseeeeeeneseeeeeeees 66 RRO S
140. tory with the Make New Folder button The default directories are saved at program close in the Registry and reloaded when you next open Fractal ViZion 5 Fine Tuning menu Fine Tuning menu commands TheFine Tuning menu offers the following commands Auto Sound Alert Enable or turn off sound alerts Auto Time Show time used to plot image Auto Random Randomize new fractal type Auto Redraw Redraw image on command Auto Clear Clear drawing area before new plot Auto Remote Open remote automatically at startup The following commands can be used via the Color menu Color Scaling menu Palette menu Divide By One Palette No split palette Divide By Two Palette Split palette into two sections Divide By Four Palette Split palette into four sections Divide By Eight Palette Split palette into eight sections The following commands can be used via the 2D Render Menu Anti Alias Use anti aliasing with 1 X4 or 1 X2 super sampling Biomorph Escape on any part of z O 2003 2010 Mystic Fractal Fine Tuning menu 36 Bioconvergence Relates Biomorph method to convergence Biomorph Off Reset biomorph flag Newton gt Define Newton method or clear Newton flag Renormalization Renormalization Convergence Color converging points with level set colors Default Function Use default function type Level Curve gt Set level curve or reset level curve flag Decomposition gt Binary or continuous decomposition Decomposition Off Rese
141. track of turtle position and variables whenever it is necessary to return to a particular point in the drawing This is useful for producing tree structures and other branching patterns Fractal ViZion puts on its stack the turtle position headings line style and color information The third significant difference between L systems and other turtle graphics interpreters is in its handling of recursion In L systems recursion is a built in feature You only need to specify the level of recursion and the Isystem does its string interpretation to that level Fractal ViZion uses recursion to call its own interpretation routines and thus eliminates the need for lengthy strings to interpret The price for the above built in features is speed Lsystems can never be as fast drawing a dragon curve for instance as a dedicated dragon drawing program On the other hand fractal generators have trouble matching the speed of L systems where branching patterns are involved There is no need to recurse backwards to reach a branching node in L systems just pop the stack and you re there Fractal ViZion is capable of rendering polygons in three dimensions but cannot match the speed of a dedicated 3 D modeler Hidden line removal is done via a z buffer with simple ray tracing to enhance the view L systems offer the user a chance to experiment with a very different approach to graphics fractal production Syntax for Fractal ViZion s Lsystem default and extende
142. tt r3 Modified Quadratic by Julian C Sprott r4 Chaotic Iterated Map r5 Chaotic Iterated Map 2 r6 Flame 1 variation of Scott Drave s Flame method Ray Tracing Window Ray Tracing Window The Light Point variables lightx thru lightz determine the direction of the light source used in the ray tracing algorithm The ViewPomt represents the angle at which the object is ray traced which can affect Phong highlights greatly This has no effect on the camera view The Lighting variables shininess highlight gamma and ambient are used to adjust ambient light and highlights The ranges for these variables appear beside their label Decreasing the shininess value increases light reflected by the object and the apparent sheen on the object s surface The ambient value controls the amount of ambient light that illuminates the object The highlight value increases or decreases the specular Phong highlighting while the gamma value increases or decreases the intensity of the light source s illumination Once a plot is started the lighting variables and light point can be changed without redrawing the object Click the Apply button to redisplay a plot after changing the lighting variables or light point Click the Okay button to close the Ray Tracing Window applying new settings if the variables were modified Click on Cancel to revert to the state that existed when the ray tracing window was opened Click on Defaults to set the li
143. tyle fractals Here you enter a character string or word that can contain any of 25 letters a through y Each letter or gene references a built in formula as defined in the Genes window For every iteration the program cycles through the character string and uses whatever formula is referenced by the characters Notes If Max Iter is shorter than the gene string then only part of the string is used For quaternions which usually have a very short iteration cycle changing Max Iter can have a dramatic effect on the fractal output The fl f4 combo boxes are used to designate the fn user definable part of a generalized function This can be one of the 41 function types listed sin w cos w etc A few of the options are formulas themselves L3 w the Legendre function the gamma function and G w the Gaussian function so quite complex though mathematically unintelligible formulas are possible The S control is used to enter the variable s used in many of the built in functions The Si control is used to enter the variable si the imaginary component for s in some of the built in functions The Converge control is used to enter the convergence limit for Renormalization or Convergence O 2003 2010 Mystic Fractal 23 Fractal Zplot Application Help plots This is a measure for how close z needs to approach an attractor to be mapped to that attractor color A small value 0001 000001 is normally used Smaller values of the conv
144. ula values to the new values The Reset button returns all boxes and slider values to their original values when the window was opened The three buttons named Rand fun 1 Rand fun 2 and Rand fl f4 are used to pick formulas functions at random Clicking on Rand fun 1 a formula is chosen from the 100 built in formulas for fun 1 Clicking on Rand fun 2 a formula is chosen for fun 2 Clicking on Rand fl f4 functions are chosen for fl f4 Select FraSZle Formulas to switch to the FraSZle formula set 4 7 Fractal Variables Fractal Variables The window opened varies with the fractal type selected and contains all the major variables that Fractal ViZion now scales between key frames of an avi stream 4 7 1 Parameters Window Parameters Window There are edit controls for entering the complex constant real and imaginary parts and the min max ranges for the real and imaginary window coordinates Fractal Zplot uses three corner plotting for easier rotating so boxes are provided for Top Left Top Right and Bottom Right real imaginary coordinates These reflect the current range values that may have been derived from zooming with the Zoom option Slider type controls affect the number of iterations 1 9999 the z limit 1 9999 Cj ck and hj are for entering hypercomplex parameters Cx cy cz and cw are used as complex C increments for Julia Tower types The Size slider controls the overall size of the picture The Size slider sets
145. vertex 2X move x forward record vertex g move forward with full length don t record vertex g x move x forward don t record vertex don t move record vertex Structure commands 2003 2010 Mystic Fractal Help menu 9 push current state pop current state start polygon shape end polygon shape jncrement length with 1 1 decrement length with 0 9 x multiply length with x also x increment angle with 1 1 decrement angle with 0 9 Xx multiply angle with x also x increment thickness with 1 4 decrement thickness with 0 7 x multiply thickness with x also x c increment color index c x set color index to x Extended command syntax r n repeat the execution of the following commands by the number specified by the following character or characters The default is 1 or one repetition For example r 5 would repeat a loop 5 times rv repeat the execution of the following commands until the current heading is reached again Used to create turtle graphics subroutines that stop when the the total turning is a multiple of 360 degrees rp repeat the execution of the following commands until the current position x y z is reached again Used for mapping lissajous curves end of repeat loop Repeat loops can be nested to a level of 10 You should begin and end a repeat loop inside of the same production rule or axiom to avoid potential problems with the interpretation of that l
146. wing Fractal ViZion displays the Save As dialog box so you can name your drawing To save a drawing with its existing name and directory use the File Save command Load button Load button Use this button to open an existing data image file in a new window You can open multiple image files at once Use the Window menu to switch among the multiple open images Bmp radio button BMP radio button Use this button to select the BMP format when loading and saving fractals This is the default Windows bitmap format readable by most Windows programs that use image files This is also the fastest method of loading and saving fractals but requires more disk space since no compression is used Windows keeps track of the last six BMP files saved or loaded displayed in the Files menu Png radio button PNG radio button Use this button to select the PNG format when loading and saving fractals This format uses medium compression without loss of image quality Jpg radio button JPG radio button Use this button to select the JPEG format when loading and saving fractals This format uses moderate compression but with some loss of image quality Preferable for posting to the net since most browsers can display jpeg files This option uses the jpeg library written by the Independent JPEG Group Illl button lill button Through a series of windows this allows you to name and open an avi animation stream and choose a compression method After
147. xy up to 80 characters per formula Algebraic notation is supported to a limited degree E G you can enter a variable as 2x2 instead of 2 x x A and B are optional constants 2003 2010 Mystic Fractal 55 Fractal Zplot Application Help 5 10 S is an optional trig function 1 to three letters 1 will work for sine cosine and tangent but use the above abbreviations for the other functions X and Y are the standard variables The could be any of the math functions The parser interprets up to 10 levels of parenthesis Use parenthesis to separate complex expressions Use parenthesis to embed trig functions within other trig functions etc Orbit traps Orbit Traps This includes methods that trap the orbit of a point if it comes in range of a pre specified area or areas The Epsilon Cross method colors points only if the absolute value of Z real or Z imaginary 1s less than or equal to Epsilon a small value Other points are mapped at the time they blow up exceed the zlimit This produces hair like structures that branch wildly from the complex set boundaries For the Epsilon Inside option the epsilon method is applied only to points included in the set For the Epsilon Outside option the epsilon method is applied only to points outside the set The Globe method uses a circular area around the origin to map a point s orbits This produces sphere like structures The Ring method uses an area formed by two circles
148. y to open the main view window There are buttons to Play a file forwards or Backwards or forward automatically with Auto rewind repeat Click on Slow to slow down a video Each click on Slow halves the viewing speed A click on Stop freezes viewing and restores the view speed to normal playback Use the Open button to view a different avi file Use the Save button to save the file in a different compression format You must use a different name to save the file than the name that was used to open t Click on the left mouse button or any key to abort a save operation Note the view avi requester can be used to preview any multimedia file including midi files 8 12 Batch Mode Batch mode Here you set parameters for batching and saving random generated images to disk When the 2003 2010 Mystic Fractal Fractal Zplot Application Help Repetitions value is non zero up to 1000 random images can be generated and saved to disk Use a unique Filename to prevent batch files from overwriting existing image files The Scan Limit directs the program on how many scans it makes through each formula before it skips to a new formula if an interesting Julia fractal hasn t been found For lsystems the scan limit is a limit on how many mutations on the rules may be done before drawing There are check boxes that affect only random quaternions or Isystems also New If you select this option before opening a video stream then instead o
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