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.
- 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.
- 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
- 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!
- 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.
- 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.
- 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.
- 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".
- 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
- 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!