The Chaos Hypertextbook™
© 1995-2007 by Glenn Elert
All Rights Reserved -- Fair Use Encouraged
I have amassed a large collection of software available for Mac OS computers. Most of these are shareware or freeware. Some were used to create the graphics included in this book. Others were used for inspiration or entertainment. Recommended programs are highlighted in yellow. Files archived on this server were compressed using StuffIt 5.5.
dynamical-systems, fractal-dimension, ifs, l-systems, mandelbrot-julia, music, newton, terrain, miscellaneous, screen-savers
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1D Maps. James D. Meiss. 2001. James D. Meiss [external link] Seven different folded mappings (logistic, cosine, cubic, exponential, tangent, tent, and circle map). Five different ways to analyze them (cobweb, bifurcation, lyapunov exponent, invariant density, and exit time plot). Interesting in a limited sort of way. Also available in a version for the Classic OS. |
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ABC map. James D. Meiss. 2003. James D. Meiss [external link] A 3D map editor. An example of what I would call an "unripened" application. As the author himself warns, "This is NOT a full blown nice Mac application… and using this will possibly crash the program if you type in the wrong numbers. USE AT YOUR OWN RISK!" I concur. |
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Chaos Viewer. Lightchaos. 2002. members4.cool.ne.jp/~lightchaos/FutureBasic/FutureBasic.html [last reported url] Staz Software [referring url] Disappeared before I could download it. Can someone out there send me a copy? |
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Chaotic Flows. John Lindner, Bryan Prusha, Josh
Bozeday. 2001. CoWCPP [external link] Explore the Chua, Duffing, Lorenz, and Rössler attractors. Zoom in and out, rotate, and play with the parameters. Also available in a version for the Classic OS. One of many scientific applications for the Macintosh from the very interesting College of Wooster Computational Physics Project. Other applications at this site related to chaos and fractals include:
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Gerry's Attraction (formerly Gerry's Lorenz
Attractor). Gerry Beggs. 2004. Gerry Beggs [external link] Start with a group of points on the xy plane, run them through the right equations, and watch them congeal on the Lorenz Attractor or the less interesting Rössler Attractor. Also comes with an option that allows you to fly around the attractors while they evolve. An inspired way to view them. Much better than fixed diagrams. Carbonized to run in both the Classic and OS X environments. |
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Populus. Don Alstad. 2003 Don Alstad [external link] A comprehensive tutorial on population and evolutionary dynamics with something like 20 different models to play with. The help files are more interesting than the program itself, however, which hesitates in the most annoying manner. Still has a lot of potential as a great teaching tool for undergraduate students in this field. Also available in a version for Windows, Linux, Unix, DOS and Java. (The OS X version is actually just a "packaged" Java application.) |
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StageGrow. Ian G. Gillespie. 2001. Ian Gillespie [external link] A program for exploring population dynamics in a single species. Very technical. Designed for people who know what it's all about (which excludes me). Staged, geometric, exponential, and logistic models are supported. |
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StdMap. James D. Meiss. 2002. James D. Meiss [external link] Standard map orbits in this book were drawn using the Classic version of this program. Has other features for exploring nine different area preserving maps. A nice piece of software with good documentation. Fast and fun to play with, too. |
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Fractal Grower. Joel Castellanos. 2007. Joel Castellanos [external link] Java software for growing L-systems fractals. Being Java means it works on multiple platforms, including the browser you're using to view this web page. Make your own system or use one of the many presets (paper folding, bush, carpet, dragon, fern, big-h, twig, weed, koch snowflake, sierpinski triangle, etc.). |
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FractalTrees X (also known as FTX). Simon Woodside. 2002. Simon Woodside [external link] Draws simple stick figure, fractal trees. Comes with an easy to operate set of sliders for changing parameter values. Orders of magnitude better than the original Classic application. The author is also working on a screen saver version called FTXSaver. |
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iFractales. Didier Straus, 2005 Software-DS [external link] Draws 9 different fractal figures including the Koch snowflake, Sierpinski triangle, and Peano and Hilbert curves. |
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VonKoch. Julien Salort. 2003. Julien Salort [external link] A simple, little program for drawing the Koch snowflake and its variants. |
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AltiVec Fractal Carbon. Dauger Research. 2001-2004. Dauger Research [external link] A program for testing the computing power of a distributed computing network. Generates images of the standard and quartic Mandelbrot sets, then tells you the speed of your parallel processor network in megaflops. If you only have one computer, then it tells you the speed of just that computer. Allows you to zoom in and that's about all. Comes with very few options as it is primarily a benchmarking tool. Also available as a Classic application with no options -- zero. It runs and it's done. |
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Carbon Fractal. Harold Cooper. 2001. physoft [last known url] carbon-fractal.sit [ 20K] It appears as if it just draws Mandelbrot and Julia sets, but the website claims it has additional features. It doesn't really matter as it is too slow to be much fun. Simple programs like this one should run fast and be intuitively obvious to operate. This one is neither. |
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Cheap Mandel. Conor McCarthy. 2002. Conor McCarthy [external link] Examine the Mandelbrot set. A beginner's attempt at programming for the Mac. The original Classic OS version was not much better. |
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Complex Explorer. Thomas Hallock. 2002. Thomas Hallock [last known url] A very simple program for exploring the Mandelbrot set. Comes with a unique color palette editor that I really like. Allows the user to save coordinates, but not images. A version for the Classic OS apparently exists, but I've never tested it. |
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Dynamics. Richard Koch, Pierre d'Herbemont. 2001. Richard Koch [external link] A very basic fractal set explorer. Zoom and pan around a colored Mandelbrot set in the main window. View the associated black and white Julia set in a side window. A bit slow, given all the speed claims for OS X native applications. |
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EasyFractal. Berkhan Software. 2004. Berkhan Software [external link] Zoom into the Mandelbrot set, check out the corresponding Julia set, play with the colors, try a different function. Comes with a collection of preset parameter files, some of which are interesting and rather unusual. Available in German and English versions for both the Classic OS and OS X. |
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EDFractal. Edward Baskerville, ED Development. 2001. ED Development [last known url] edfractal.sit [117K] The first chaos/fractal application written for OS X that I found. Explore the Mandelbrot set. Create Julia sets and explore them, too. A very straightforward example of programming. |
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FFFF - Fast Floating Fractal Fun. Daniele Paccaloni. 2005. Source Forge Developer Profile The crude beginings of an application that draws the Mandelbrot set, allows you to zoom in (but not out), rotate the color scheme and a bit more. Runs in terminal mode on OS X. Very speedy. Also available in a Windows version. |
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Fractal Domains (formerly FracPPC). Dennis C.
De Mars. 1994-2004. Fractal Domains [external link] Explore the Mandelbrot set. Switch to the accompanying Julia set. Zooming in and out is rather tiresome, but otherwise this is a fine application. The switch from the Classic version to OS X has brought about a much improved look and feel. |
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Fractale de Julia, Fractale de Mandelbrojt (a.k.a. Fracatle
Julia, Fracatle Mandel), Didier Straus, 2002. Software-DS [external link] Student programming projects that don't work. Draws a filled Julia or Mandelbrot set, then quits (or never completes the startup process). These application should not have been made public. They are effectively locked in an alpha phase of arrested development. |
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Gaston. Leo Fink. 2003. gaston.sit [115K] A nice little program that renders three dimensional cross sections of quaternion Julia sets. A quaternion is a type of complex number with four parts (r, i, j, and k) rather than two (real and imaginary). Adjust all four parts of the quaternion constant with sliders. Try different escape radii until you find an interesting looking surface and export it as a TIFF. Also has sliders for adjusting the precision and resolution. Given the complexity of quaternion mathematics, you will want to keep the resolution low during casual exploration. High quality images are rendered very slowly. My only complaint is that the sliders are somewhat crude and hard to adjust finely. There should be some method for enetring the constant values directly. |
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Mandel Blot. Nixanz. 2002. nixanz.com [external link] Amateur night at the Mac. Draw and explore the Mandelbrot set. Drag to zoom in, poof, the image window disappears, poof, the image window reappears with your new image. Very simple color options: your choice of red, green, blue, cyan, magenta, or yellow with varying brightness and contrast. Note how the author has chosen to hide behind a screen name. |
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Mandel Bot. Robert Covington. 2003 Artly There [external link] According to the author, "A simple Mandelbrot viewer based on a demo by Robert Purves." Quite right. |
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Mandelbrot. Christoph Lauer. 2002. Christoph Lauer [external link] A painfully slow Java program for exploring the Mandelbrot set and rendering corresponding Julia sets. Java is not the right environment for applications that require intensive calculation. Also available for Linux and Windows. |
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Mandelbrot. David Ross. 2001. David Ross [last known url] An easily forgettable program. Draw and explore Mandelbrot sets from order 2 through 59. This may sound impressive but really isn't. Very high order Mandelbrot sets all look like circles. Switch over to the Julia set associated with a particular location of the Mandelbrot set. Very simple and plain color schemes. |
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Mandelbrot on Cocoa. SADA. 2004. SADA [external link] Explore the Mandelbrot set. Zoom in. Zoom out. Adjust the color scheme. Save your results as png files. A nice simple little program. Also available in a Windows version. |
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Mandelbrot Viewer (a.k.a. Custom View). Michael C Thornburgh. 2001. Mr. Mike [external link] A good basic Mandelbrot explorer. Simple and fast with very few options. Zoom in, but not out. Adjust the escape radius, number of iterations, number of threads (not quite sure what that means), and location of the origin (which renders distorted Mandelbrot-Julia hybrids), but not the color scheme. |
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mandelPath. Aaron Golden. 2003. Aaron Golden [external link] Doesn't draw the Mandelbrot set in the traditional manner (counting the number of iterations to escape). Instead it traces the orbit of points in the complex plane. As the author says, "It's not particularly useful but I think the pictures are pretty." This program has to be run through a terminal window. Very odd. |
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PhoenIX. Adrian Platts. 2001. Adrian Platts [last known url] Deliberately styled interface with options, options, options. Auto zooms, generates relief maps, makes movies, plays background MIDI and MP3 files, and acts as a screen saver. It also draws several kinds of Mandelbrot and Julia sets. Comes with yet more options that I haven't described. Also available in a version for the Classic OS. |
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TransWorld (a.k.a. WindowFreak). Junzo Sato. 2001. Junzo Sato [external link] A waste of time. Very slowly renders a very low resolution image of the full Mandelbrot set or one specific Julia set in a transparent window. No zooming. No variations of any sort other than the transparency level (thus the name TransWorld). A "look what I can do" application that is of interest to no one. |
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NewtonFractal. Stefan Messmer. 2001. Stefan Messmer [external link] Draw fractals using Newton's root approximation method in the complex plane. Faster and more reliable than the original Classic application, but still looks and acts like a beta edition in need of a solid debugging. Also available in Windows and Java versions. |
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Cosmos3d. Jeff Biggus & Heinz Nabielek. 2004. osx.hyperjeff.net [external link] A program whose sole purpose is to render Hoyle's galaxy clumping model as mentioned on page 218 of Mandelbrot's The Fractal Geometry of Nature. A good fractal for those interested in the history of cosmology, but I think Hoyle's model was disproved by galactic surveys. |
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MojoWorld Generator Demo. Ken Musgrave, Pandromeda Inc. 2002. Pandromeda [external link] A surrealistic (super-realistic?) landscape generator. A sophisticated, commercial application that is not for the casual user. The gallery of images on the company's website hints at the possibilities for someone willing to put in the time and effort: mountain ranges, beaches, rivers, clouds, sand dunes, moons, entire planets. Also available in a version for Windows. |
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Cellular. Christian Grunenberg. 2001. Christian Grunenberg [external link] A program essentially designed to investigate cellular automata that also happens to draw Mandelbrot sets and model galactic collisions. Not bad, but nothing special. |
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Escape (a.k.a. EscapePPC). Graham Anderson. 2004. EscapePPC [external link] A comprehensive application for exploring over 20 different types of fractal images and strange attractors. Unregistered versions can only render Mandelbrot sets, however. Many, many features to explore for those with a serious interest. Carbonized to run in both the Classic and OS X environments. (Not to be confused with EscapeFractals: a Newton's Method application for the Classic OS.) |
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Gerry's Mandelbrot Set. Gerry Beggs. 1998. Gerry Beggs [external link] More than just the Mandelbrot set, it also creates Julia sets, IFS images, a fractal tree, the Lorenz attractor, bifurcation diagrams, Newton's method, and Martin's mapping (a.k.a. hopalong). Gives you the ability to check out a lot of different fractals using just one application. Very fast. Also available in a version for the Classic OS. |
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Apfelmaennle, Huepfer. Heiko Kretschmer. 2002. wurst-wasser.net [external link] Apfelmaennle draws the whole Mandelbrot set, selects a region, and then magnifies it. Selects a subregion and magnifies that. Keeps going and going. I've never run it long enough to see it run out of steps, but eventually it must. According to the author, Huepfer is "One more screen saver displaying fractal-like graphics known as Hopper or Hüpfer." He does not explain what this is, however, nor have I ever heard of it before. Sometimes it looks like a diffusion pattern, sometimes like a checkerboard. Apfelmaennle is the better of the two programs. |
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Amseq. André and Paul van der Kouwe and Thomas Benner. 2003 Thomas Benner [external link] Amseq stands for "Animated Mandelbrot Sequence Generator". There is no documentation to explain what it does, but it appears to trace the orbit of points in the complex plane through successive iterations of the quadratic mapping. Recall that the Mandelbrot set is the set of all points that don't escape to infinity after an infinite number of iterations of the quadratic mapping. This screen saver draws the path of the points used to draw the Mandelbrot set, not the set itself. |
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Coral, Flame, Hopalong, ifs. Tommaso Pecorella.
2001, 2002. Uselesssoft [external link] Open source Unix programs written in the late '80s and early '90s transformed into screen savers for OS X. Coral fills the screen with DLA (diffusion limited aggregation) fractals that look something like corals when shaded in. Flame draws "weird cosmic fractals" (whatever those are). Hopalong draws the scribbly fractal of the same name plus Martin's Method, Renaldo Recuerdo (called RR), and EJK fractals (whatever those are). ifs draws an iterated function system that evolves smoothly over time. The latest addition to this group, ifs is by far the best. Using Hopalong to save your screen seems risky as it renders images that stay static on the screen for long periods. |
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FTXSaver. Simon Woodside. 2004. Simon Woodside [external link] FTX means FractalTrees X -- the name of an application from which the screen saver was derived. Draws simple stick figure, fractal trees that evolve on the screen. Still in the alpha phase but has potential. Looks like it will make interesting images, but is just too computationally rough in its current form. |
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Fracture. Stick Software. 2001. Stick Software [external link] A screen saver for OS X that creates a wide variety of fractal images: Mandelbrot set, Julia sets, Newton's and Halley's root approximation method, etc. Pleasant color schemes and rendering techniques. Interesting yet innocuous, which is what a good screen saver should be. |
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Hénon. Marco Coïsson. 2003. Marco Coïsson [external link] This screen saver gives a graphical representation of the so-called Hénon correlations. Simple and uneventful. Available in English and Italian versions. |
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IFS3D. David Leppik. 2001. David Leppik [external link] Flies over and around an evolving IFS fractal, but I don't like the way it looks. The animation isn't smooth and the images are unnaturally dim. |
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Sierpinski 3D. Epicware. 2001. Epicware [external link] screen saver of a flying, tumbling Sierpinski pyramid. Part of an Open GL bundle of OS X screen savers. |
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Xeverywhere. Stéphane Sudre. 2000-2002 White Box [external link] Start with a cube, replaced it with smaller cubes, replace the smaller cubes with even smaller cubes, and so on, then work backward. Comes with a warning not to set the number of iterations too high. Take it seriously or the Xeverywhere will seize control of your CPU. |
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