Fractals, Chaos and the Mandelbrot Set Workshop - Pt. 5

InfoPak Computer Programs Description

Here is a short description of the programs that are available on the disk that accompanies the InfoPak. The first four were written by me, and can be considered freeware. Most of the programmes have detailed explanation screens describing the processes that they illustrate. Try running them with different values and explore! They will all run, menu driven, directly off the floppy. Nothing is zipped, and nothing has to be installed. When you get the disk, type "menu" or "go" at the A:>_ DOS prompt and you're off! It will run faster if you copy the whole thing to your hard drive, but you can do that later. :-) I would be glad to hear from you, and will consider minor custom programing or sharing the source code.

  1. Chaos Game : Explains the basic idea of combining randomness and iteration to produce a complex pattern. It lets you play three, four or six corners, fractional three corners, and has good explanation screens. It is the perfect tutorial for introducing the study of chaos at any level. E-mail me and I'll send it to you directly.

  2. Population Simulation : This program is a population growth model. It illustrates the ideas discussed on pages 69-80 in Chaos, The Making of a New Science, or chapter 3 in Turbulent Mirror. See fantastic compelxity arise out of an extremely simple math formula repetition. It's what bug poplulations really do!

  3. Orbit and Dwell of Mandelbrot Set Points : This program tracks the orbit and dwell of points in and out of the Mandelbrot Set. It's really fun to watch the incredible behaviour of certain points. Some points are resolved as in or out very quickly, and some exhibit wonderfully fascinating behaviour. You'd swear the numbers where "alive" and spinning spider webs! The (x,y) points -.5111 and -.5111 take the longest to calculate before they "explode". (2561 iterations) Search for other coordinates on the fringe of the Set, and e-mail me if you find any that take longer. A fractal image button to anyone who finds one!

  4. Numeric Values of Mandelbrot Set Points : There are dozens if not hundreds of programs that create beautiful images of the Mandelbrot Set. Wanting one that displayed the numbers that resulted from iterating the famous z = z^2 + c equation, I ended up having to write my own. This program doesn't produce a pretty picture, (it does show the set) but it's the only one I know of that lets you track the numeric values. It's good for giving you a feel that you can really see what's going on as individual pixels are calculated to be in or out of the Set.

  5. Mandelbrot Magic v4.0 : The is a full featured, powerful program that generates the Mandelbrot Set and Julia Sets. The documentation in the .DOC file is 60 pages long. This is shareware from the folks at Left Cost Software. If you keep it, please register with them.

  6. Koch Snowflake : Displays the famous von Koch snowflake, a classic fractal curve. This unique shape has a perimeter that increases to infinity, while the area remains finite. This program (and also #'s 7, 8 & 9) is an .exe file compiled from the code in "Fractal Programming In Turbo Pascal" by R. T. Stevens. It includes a small tutorial that explains the iteration process that generates the curve.

  7. Lorenz Attractor : Displays three views of the Lorenz attractor. The Lorenz attractor is described in almost every book on chaos or fractals. It is best described in the NOVA video, "The Strange New Science of Chaos".

  8. Four Ferns : Demonstrates how a rule more complex than the Chaos Game, combined with iteration, can lead to a complex natural shape. This is the heart of the "secret" of how nature builds such complex and elegant natural structures.

  9. Bifurcation Diagram : Displays the period doubling route to chaos, or the Verhulst process. This program is the summation, or the "attractor" of the population dynamic that is illustrated in detail in program #2, "Population Simulation." Once you know what you are looking at, (and it takes some thought to make sense of it) the complexity that arises out of the simple dynamic of iteration is truely mind-boggling!