6. Fractal programs

 6a. What are the most frequently used programs for complex polynomial fractals? 6b. What are the most frequently used programs for quaternions? 6c. What are the most frequently used programs for L-systems? 6d. What are the most frequently used programs for flame fractals? 6e. What is the most frequently used program for 3D IFS? 6f. What program can be used for fractal landscapes? 6g. What are the most frequently used programs for fractal music? 6h. Are there other programs of interest? 6i. Where can I find more complete lists of programs?

 6a. What are the most frequently used programs for complex polynomial fractals?

 6b. 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. Quat 1.11 http://www.physcip.uni-stuttgart.de/phy11733/quat_e.html#Download Freeware, sources available. 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. The quaternion package CD http://www.hypercomplex.org/cdinfo.htm Commercial (sold on a CD). 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. Terry W. Gintz’s downloads http://fractals.iut.u-bordeaux1.fr/terry/ and http://www.eclectasy.com/twg/default.html Freeware, sources available.    KPT (was Kai’ Power Tools) is  a powerful graphic plug-in for PhotoShop (Windows and Macintosh). It had a module named  Frax4D for quaternions. KPT http://www3.corel.com and search for Frax4D Commercial.

 6c. 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): Laurens Lapré’s Lparser http://home.wanadoo.nl/laurens.lapre/lparser.htm followed by Povray post-processing. Lparser has a mutation algorithm to get random variations from a starting object. Freeware, sources available. LSys32 http://chris.lichti.org/Lab/LSys32/LSys32.shtml) by Christopher C. Lichti is a windows shell to use easily Laurens Lapre’s Lparser. Freeware.  L-system 4 http://www.thinkpiece.com/thinkpieceDT1.asp?iNode=19& pageMode=displayNode by Bryan Smith is a Windows program which generates DFX files to export into ray-tracing programs. Freeware. Dofo-Zon http://fractals.iuta.u-bordeaux.fr/terry/ and http://www.eclectasy.com/twg/default.html has a L-system module with a mutation algorithm and basic ray-tracing capabilities integrated. Freeware, sources available.

 6d. 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. KPT http://www3.corel.com and search for FraxFlame Commercial. Qsflame http://www.uvm.edu/~msargent/main.htm is a program by Michael Sargent that uses an algorithm from Scott Draves, who discovered this type of strange attractors Freeware.    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. Cold-IFS, Atriatix http://www.eclectasy.com/Iterations-et-Flarium24/ Freewares, sources available.

 6e. 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. XenoDream http://www.xenodream.com/ Commercial.

 6f. 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. Bryce  http://www3.corel.com/ and search for Bryce Commercial. Terragen (http://www.planetside.co.uk/). Free for private use.    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. Pandromeda site (http://www.pandromeda.com). Commercial.

 6g. What are the most frequently used programs for fractal music?

 6h. 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. http://www.cygnus-software.com/index.html Commercial. 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.  http://www.eclectasy.com/Fractal-Explorer/index.html Freeware. 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. http://www.chaospro.de/index.html Freeware. 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. http://skyscraper.fortunecity.com/terabyte/966/download.html Freeware. 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). http://www3.corel.com Commercial.   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  ftp://ftp-hs.iuta.u-bordeaux.fr/fractorb/ and at Spanky - Noel Giffin http://spanky.triumf.ca/pub/fractals/programs/ Freeware. For quaternions Besides the programs cited previously, the Quaternion Generator program by Frode Gill (Windows, 16 bits) is always available at: Frode Gill Home page http://home.hia.no/~fgill/ Freeware, sources available. Fractal Explorer by Sirotinsky A.A. and Fedorenko O.V. (see above) Fractal Explorer Homepage http://www.eclectasy.com/Fractal-Explorer/index.html MMFrac by David Makin (see above). http://skyscraper.fortunecity.com/terabyte/966/ Freeware. KPT 5 http://www3.corel.com Commercial. For L-systems We have no experience of the following program but nice images can be seen on the site: LinSys3d by Andrea Esuli http://www.geocities.com/aesuli/LinSys3d/ Freeware. For terrains Having no personal experience we suggest to look at the list and short descriptions at the Joe Slayton’s page: Terrain Bits http://www.ridgenet.net/~jslayton/terrain.html Fractal Explorer (see above). Fractal Explorer Homepage http://www.eclectasy.com/Fractal-Explorer/index.html MMFrac by David Makin (see above). http://skyscraper.fortunecity.com/terabyte/966/ Freeware. For  fractal/generative music ArtSong http://www.artsong.org Shareware. A Music Generator http://www.musoft-builders.com/ Shareware. Oblivion http://tinpan.fortunecity.com/fluke/807/ Freeware. Tapestry MIDI Studio http://www.quantumportal.com/ Freeware (?). Mandelbrot Music http://www.fin.ne.jp/~yokubota/mandele.shtml Freeware.

 6i. Where can I find more complete lists of programs?

 A well documented list of freeware programs is maintained by Juan Luis Martínez: Third Apex to Fractovia (http://www.fractovia.org/fractal_generators/fractals_freeware.html). The most exhaustive list is maintained by Paul N. Lee: Fractal Links on Paul N. Lee’s website (http://home.att.net/~Paul.N.Lee/PNL_Fract_Sftw.html) A very great numbers of programs can be downloaded from: Spanky (http://spanky.triumf.ca/pub/fractals/programs/) and mirror site (http://spanky.fractint.org/)