6. Fractal programs 

Table of contents



What are the most frequently used programs for complex polynomial fractals? 



What are the most frequently used programs for quaternions? 



What are the most frequently used programs for L-systems? 



What are the most frequently used programs for flame fractals? 



What is the most frequently used program for 3D IFS?



What program can be used for fractal landscapes? 



What are the most frequently used programs for fractal music? 



Are there other programs of interest? 



Where can I find more complete lists of programs? 







What are the most frequently used programs for complex polynomial fractals? 

Fractint (Stone Soup Group)

   Fractint was the first great fractal program. It appeared in 1988 under the name FRACT386, and version 6 was renamed FRACTINT in February 1989. Its name originated from the fact that it emulated floating point math, which was slow at that time (many computers did not have coprocessors) by a fast-integer emulation, together with a floating-point algorithm to support coprocessors (but for a long time the default mode was the integer one).
   Fractint has an invaluable deep-zooming capability which overcomes the limitations of the coprocessor double-precision mode (which “limits” the zoom to approximately 1015 times) by using an arbitrary-precision algorithm. But this mode is very slow because it does not use the coprocessor and it is not compatible with all types of fractals. In the usual range of zooming, Fractint uses double-precision variables.
   Fractint is a freeware. It is a collective work of many contributors which are known as the Stone Soup Group. At present, the development is under the responsibility of Tim Wegner.
   Fractint has been the leader in fractal creation for a long time, and it incorporates a great number of powerful and extensive options which have largely inspired more recent programs. Particularly, it has a fast parser which allows very complex formulas, especially when conditional tests were added to its capabilities. All the classic, and many more modern features of fractal rendering were introduced in the successive versions of this program.
   However, Fractint has some limitations: it is a DOS program with an outdated interface and it uses only the 256 color mode. Nevertheless, after a few times of use, this interface becomes very easy to use.
   Until recently Fractint was the most widely used program, and for many years, almost all fractal art was developed with it. It is still supported by many artists (even if they also use more recent programs) because thousands of formulas have been published and are available, and because the syntax to write these formulas is a quasi standard.
   The latest version 20.0 is dated 1999 and can be found, together with invaluable information, at the

   A Unix port named Xfractint is available from the same page.
   The Windows version, named Winfract, is quite old and limited.

Ultra Fractal (Frederik Slijkerman)

   Ultra Fractal 3 is a powerful shareware program created by Frederik Slijkerman, whom was helped by suggestions made by Damien Jones. It runs under Windows 95/98/NT/2000/XP and it produces true-color images. Contrary to other programs, it has very few built-in fractal types: most fractal types are implemented as formulas that are compiled on-the-fly. Ultra Fractal’s parser is fast: before they are executed the formulas are compiled to Pentium assembler code.
   One principle of this program is to run together 3 categories of separate formulas: the fractal formula itself, the color formula and, possibly, transformation formulas (for global transformations of the image, like twisting, mirroring, kaleidoscope, and others).
   Thousands of compatible formulas are available because most of the Fractint formulas can be used and because many artists use this program. However, some users have reported a few incompatibility problems with Fractint formulas.
   New formulas are published almost every week (as of today, 31 Mb of formulas are available).
   This program has an original solution, named gradient, to  define the colors of a fractal. A gradient consists of any number of control points (RGB or HSL colors) that are interpolated linearly or smoothly to create the true-color equivalent of a 256-color palette. Many users find this approach very handy, while others think that it is not as easy as the classic palette approach.
   Ultra Fractal can mix images drawn in any number of separated layers in a controlled way, like Photoshop. This offers a field for new artistic effects. Anti-aliasing and rendering of very large images to disk is incorporated.
   Ultra fractal is limited to the creation of complex polynomial fractals, although Stig Petterson has written formulas which can draw 3D quaternions. It uses 80 bits of precision, which enables it to do deeper zooming than most other programs without loss of speed and, for higher magnifications it switches into arbitrary precision (similar to the deep-zooming mode of Fractint).

Stephen Ferguson’s programs

   Stephen Ferguson has written several fractal programs (all for Windows and true color). The most well-known are Iterations (the first), Flarium 24, TieraZon, TieraZon 2, GrafZViZion, and Sterling-Ware. The most recent are Vchira and Katza. He was perhaps the first to clearly separate into different menus the fractal formulas, the rendering formulas, and a final transformation by algorithms he named “filters”. Those 3 steps were written as plug-ins for TieraZon 2 and these plug-ins are shared with DofoZon, a program by Terry W. Gintz (see below).
   Stephen Ferguson’s programs use a quite original color controls. The user does not build the palette by choosing the colors himself, but by setting several parameters which make the three colors (Red, Green, Blue) evolve independently in an algorithmic way according to a triangle wave function in the first programs and a sine/cosine one in the latest ones. In these programs the characteristics of each color channel can be controlled in various ways by several settings. Colors are more difficult to control than with a palette but very original effects can be obtained, which explains why many fractal creators are interested in these programs at the present time. No help files are provided in the later programs.
   The programs use double precision variables (64 bits).

Terry W. Gintz’s programs

   Two  programs are currently available: Dofo-Zon Elite and FractalViZion. These programs go back almost to the beginning of Fractint, though the development proceeded independently on an Amiga 2000 (1989). Much of the same formulas/rendering techniques were used, based on classic fractal texts. Therefore, when the two programs “met” in PC format, the author was able to simulate many of Fractint’s featured rendering methods, built-in formulas and parser options.
   Fractint-compatible parser/loader: most Fractint v18 and v19 escape-type par/frm files will load and draw. The current programs run on Windows 95/98 (not tested on NT).
   Dofo-Zon Elite was produced in collaboration with Stephen Ferguson, so it shares the same plug-ins as the Tierazon-series programs, as well as dual coloring modes, palette-based and his rgb coloring mode.
   Features: Context help for every menu item and dialog window. Formula mixing/translating that includes IFS, composite fractal types (piping one formula into another) and Escher-like tilings. Built-in Paul Carlson stalks/bubble methods work independently of any of the 100+ built-in formulas or user-defined parser formulas. Built-in formulas and rendering methods from Earl Hinrichs and Sylvie Gallet. Large number of built-in 3D fractal types, including quaternions, lsystems, orbital fractals and 3D height fields. Fast quaternion generator (z-buffer enhanced), ray-traced with Phong highlights and coloring formulas (as per Dirk Meyer’s Quat). Hypercomplex extensions for nearly all built-in formulas and parsed formulas. Random fractal options, for semi-automatic fractal creation, and batch processing. Built-in filters based on Stephen Ferguson’s ones. True color with a palette editor similar to Fractint’s. HSV filtering to extend the coloring range of images beyond what’s possible with palettes alone. Audio/Video support: most fractal types can be animated as a series of images stored in an avi file. Anti-aliasing. There an optional ŕ la Fractint parameter window. Up to four figures (layers) can be merged inside the program.  Non-3D fractal data can be converted to midi files.
   The program/parser isn’t assembly-language optimized (the built-in “fast” Mandelbrot/Julia option includes an assembly-language version by Damien Jones). With current processor speeds, the lack of assembly language usually isn’t a problem, but the programs have always emphasized flexibility and user-interface over speed. No deep-zooming support. The programs use double-precision variables (64 bits).
   Because the original program tended to overwhelm a first-time user with a plethora of menu options and parameter windows, Fractal ViZion was designed to augment a novice fractalist’s first attempts at fractal making.  FV uses a pop-up tv/remote control interface and automatic random-fractal generator to simplify fractal creation, and batch modes for unattended explorations of several fractal types: Julia sets, 3D and hypercomplex, etc.

Mind-Boggling Fractals

   Mind-Boggling Fractals is the first Paul Carlson’s publicly released program (2000). Paul Carlson is the inventor of the orbit trap rendering methods.  The program features a very easy-to-use user interface that makes it suitable for fractal novices. Images are created and saved as standard PNG files, eliminating the need for intermediate files.
   The program includes user-defined equations, and also has 35 built-in equations and 20 built-in rendering methods with the ability to instantly change the combination of equation and rendering method. It includes a simple color map editor designed specifically for orbit trap rendering methods

Fractal Domains (for Mac, by Dennis C. De Mars)

   Fractal Domains is a shareware program for Power Macintosh that generates fractal images. Fractal Domains generates color images of:

Mandelbrot set and associated Julia sets
Fractal formulas based on rational functions (ratio of two polynomials)
Newton and Halley fractals based on arbitrary rational functions

   The program also contains extensive support for orbit traps and alternative criteria for determining colors (in addition to dwell count, color can be based on continuous potential, angular decomposition and distance estimation). Other features include editable color maps, a preview window, and the ability to “spool” very large images to disk (fractals much larger than available RAM may be generated). It was one of the first programs to incorporate anti-aliasing.
   The program uses double precision variables.


What are the most frequently used programs for quaternions? 

Quat (Dirk Meyer)

   Quat is perhaps the most well-known program to draw 3D quaternions. Basically it is a command line program, but it has a graphic interface for Windows and for Linux XWindows. Quaternions are drawn in true color mode and are ray-traced.

The quaternion package(Terry W. Gintz and Godwin Vickers)

   Godwin Vickers and Terry Gintz have released a CD which includes  QuaSZ, Cubics, Fractal Zplot and QuatPOV.
   QuaSZ graphs 3D slices of formulas based on 4-D complex number planes. QuaSZ currently supports quaternion, hypercomplex, octonion and cubic Mandelbrot renderings of the Mandelbrot set and Julia sets. The complex math functions supported include sin(z), sinh(z), zz, ez, zn, sqrt(z), cos(z), cosh(z), tan(z), tanh(z), log(z), ln(z), nz and others. Random image generators and a random formula generator, batch mode and integrated video routines make the program easy for beginners and a powerful complement to advanced fractal artists.
  The random menu allows to scan all the built-in formulas to find good quaternion shapes. The Random Formula Generator allows up to 10 levels of randomization to create random quaternion formulas. Combined with QuaSZ's random scanner only the good formulas will be used.
   Also, there are mapping options that use non-traditional methods, such as composite formulas and IFS (Michael Barnsley). Quaternions can be exported as OBJ (Alias|Wavefront) or WRL (VRML 1.0) files

Note that Fractal Zplot is no longer a freeware.

Other programs

b>Dofo-Zon (already mentioned) can draw 3D quaternions, hypernions and even 3D cubic polynomials. The initial quaternion engine incorporated in these programs was Frode Gill’s one, but it was later improved to be faster and has now some characteristics more or less similar to Quat.

   KPT (was Kai’ Power Tools) is  a powerful graphic plug-in for PhotoShop (Windows and Macintosh). It had a module named  Frax4D for quaternions.



What are the most frequently used programs for L-systems? 

   Fractint supports a graphic L-system language which has been widely used in several tutorials to demonstrate the capabilities of this type of language. But the rendering is limited to the drawing of straight segments. It is possible to draw interesting figures, but they are not very spectacular.
   There are better programs  (outputs need to be post-processed by ray-tracing programs):



What are the most frequently used programs for flame fractals? 

   KPT is  a powerful graphic plug-in for PhotoShop (Windows and Macintosh). It had a module named  FraxFlame with which some artists have obtained very great flame fractals.

   Stephen Ferguson has developed a set of programs (including Cold-IFS and  Atriatrix) that use Scott Draves’ flame algorithms, expanding on them in different ways, with  other formulas and concepts.


What is the most frequently used program for 3D IFS? 

   With XenoDream Garth Thornton and Virginia Sterling have opened a new an spectacular domain in fractal art. XenoDream is a flexible environment incorporating 3D object creation, 3D lighting and filters, 2D layering and various other operations. One of XenoDream's strengths is in quickly producing 3D objects that are different from anything you've seen before. You can explore infinite realms of strange and beautiful shapes of every type, familiar or abstract, solid or nebulous, simple or intricate. The rendered fractal is not complete until 3D lighting has been applied. By combining 3D lighting with other filters in one step, a huge variety of effects is possible. As well as standard lighting effects you can get diverse materials such as metals, plastics and rocks, artistic styles such as pencils, paints and woodcuts, and many that defy description.


What program can be used for fractal landscapes? 

   We have no personal experience in this domain. We know only that Bryce, a program for Windows and Macintosh (from Metacreations, but now owned by Corel) uses algorithms created by Ken Musgrave, and this is a great reference.
   Another, often quoted program is Terragen.

   Pandromeda offers programs for Linux, Mac and Windows. There are two programs: MojoWorld Transporter allows to explore and transform to some extent worlds already created (included in the program or downloaded from the site). The free version displays the Pandromeda logo on the image and the Transporter Pro is less limited and do not displays the logo  ($29.99).
   The main program, MojoWorld Generator is expensive ($249) but can create words and planets without any limitation. As we understand, here again, Ken Musgrave is behind these programs.


What are the most frequently used programs for fractal music

Tangent (Paul Whalley)

   In an approach described as “everything but the kitchen sink”, Tangent utilizes algorithmic, and heuristic, deterministic and stochastic, generative and transformational methods. Rich 16-voice polyphonic, elaborate musical structures can be created. Structures can be created from “composition-seed” values and/or by user-supplied melody strings. An instruments page allows for the setting of most MIDI instrument parameters, plus the options to emphasize bass, amount of relative accompaniment, compositional and complex compositional performance  devices for each instrument, and identifying an instrument as a “bass” or “poly” track.
   Tangent compositions are divided into sections called “periods”. The Period parameter page is where the tune is composed. This can be done automatically from the composition seed, then edited. Period parameters include period length, main/number of bass/poly tracks, melodic material selection, probabilities of rest/compositional device, transposition, and beat pattern reduction. Periods may be cut and pasted at will. Tangent offers an almost immediately-useful interface, and also a great deal of depth to be explored by the experienced. Tangent excels at producing fast-paced neoclassical-style music, but almost any genre can be created with some experimentation.

Gingebread (Phil Thompson)

   The Mandelbrot/Julia sets are the basis for music created with Gingerbread. The main user interface is a pane of 16 “Mandelbrot-browser” windows, each representing an instrument. All standard MIDI parameters are available to the user. In addition, chording, repetitions, GS MIDI parameters, and Roland Sound Bank variations may be used. Actually hearing the MIDI extensions depends upon one’s soundcard / equipment setup.
   For composing the piece Gingerbread has a “bar lab”. A spreadsheet-like grid consisting of 128 vertical columns, each representing a bar of music. Any Gingerbread parameter may be changed at any bar, allowing for variety. In addition there is an “image-processing” facility where the RGB parameters of a bitmap are used to determine certain instrument parameters; a “randomizing” page to auto-generate the bar lab values, and a wave-file looping utility for playing back a wav file for accompaniment.
   Gingerbread is a full-featured music composition system. Results come with exploring and learning to use it’s many features, especially the bar lab.

QuasiFractal Composer (Paul Whalley)

   QuasiFractal Composer is the predecessor to Tangent. Many of Tangent’s concepts were built upon QFC. Still a valid composition tool for the 21st century, results are more unpredictable than with Tangent, as there is not as fine a control over the composition.
   All standard MIDI parameters are supported in QuasiFractal Composer. QFC is built around composition “structures”, including glissando/pointillism, periods, phrases, rhythms, dynamics, repetitions, and phrase and period lengths.
   Very interesting, and often very surprising compositions can be created with QFC.

MusiNum (Lars Kindermann)

   This software offers a very easy to use interface, and can yield quite interesting results, ranging from Classical to Bizarre. Based upon the Morse-Thue algorithm, each of 16 instruments is parameterized with standard MIDI parameters as well as a number of settings that go into the algorithm.
   Immediately useful for the novice, one may explore further and compose using it’s scripting facility, whereby on an instrument by instrument basis; parameter settings changed at any “counter” values.
   This was the first Fractal Music Composition tool ever encountered by the Author, and still one of the most widely-used tools in existence today.

FractMus (Gustavo Diaz Jerez)

   The author of this answer has no direct experience composing with this software. At a glance, it seems to have a quite full-featured interface with many configurable parameters, and a “composition wizard” as well.



Are there other programs of interest? 

   The fact that these programs are listed here doesn’t imply any judgment about their interest: it is only because they are less used.

For complex polynomial fractals, and others

  • Fractal eXtreme is a program from Cygnus software, known for its ability to created static as well as animated fractals.

  • Xaos, known as a real-time zoomer gives also very good static fractal. It exists for Dos, Macintosh, Red Hat Linux, Debian Package, OS/2, BeOS, Amiga
    http://xaos.theory.org/ and http://sourceforge.net/projects/xaos/
    Freeware, sources available.

  • Fractal Explorer by Sirotinsky A.A. and Fedorenko O.V. is a Windows program which can draw all the classic types of fractals: complex polynomials, IFS, strange attractors.
    The program has about 100 built in formulas.  It has the capability to create formulas. There is a formula editor and it allows the user to generate code that is then compiled with the Delphi compiler.  Other features include the ability to create AVI video files and landscape scenes.  It uses some OpenGL and also a special 3D library from RenderLib. 

  • KaosPro 3.02 by Martin Pfingstl can read almost 80% of Fractints fractal types. The fast compiler it uses, together with the import mechanisms, allows ChaosPro to use all UltraFractal formulas (transformations, iteration formulas, colorings) and to calculate all fractals which UltraFractal can calculate.
    This especially means that ChaosPro has most of the features of UltraFractal 2.05 currently built in.

  • MMFrac by David Makin is a DOS 32 bits program written in assembly language. It draws all sorts of fractals including 3D quaternions, hypercomplex fractals and fractal landscapes.

  • KPT is a powerful graphic plug-in for PhotoShop (Windows and Macintosh). It has a module named Fraxplorer which draws complex polynomial fractals. In the Fractal Art discussion list it has also been said that KPT is 'built-in' to Corel Photopaint 10 where the fractal element is called Fractal Explorer 2.0).

  • Fractal Orbits (Phil Pickard) was the first publicly available program devoted to orbit trap methods (Windows). In spite of the fact that it is limited for the number of colors (236) and the maximum size of the images, it is perhaps the most easy program to discover these fractal types.
    It is available by FTP at 
    and at Spanky - Noel Giffin http://spanky.triumf.ca/pub/fractals/programs/

For quaternions

For L-systems

We have no experience of the following program but nice images can be seen on the site:

For terrains

For  fractal/generative music


Where can I find more complete lists of programs? 

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