THE CHAOS GAME

One of the discoveries of the new science of Chaos is that there seems to be
an underlying order in randomness. Applying the simple rule of plotting a
point from a starting position - halfway to a randomly chosen vertex of an
arbitrary triangle, using the new point as the next beginning, and repeating
produces a strikingly orderly pattern. This so-called Sierpinsky Gasket
is a figure with a dimension of less than two, a fractal dimension.

Type SIER and see the triangle drawn, the "seed" point circled. This point
may be inside or outside the triangle, it matters not. Watch as the pattern
becomes illuminated in different colors showing which of the vertices has
been selected for any given plotted point.

The source code in the file SIER.C is made available for C programmers who
wish to do their own tinkering with the patterns. The file SIER_1.C is
source code for those wishing to try a variation, using an extra
"attractor" inside the triangle. The resulting pattern at first appears
more chaotic, but soon resolves itself into a visually interesting orderly
pattern.

============================================================================

1
*
START chosen at random * *
within or outside the triangle. * *
* *
* *
2nd point halfway to * o *
(randomly chosen) vertex * 2nd *
#1. * *
* *
* o o *
3rd point halfway to * START 3rd *
(randomly chosen) * *
vertex #3. 2 ************************** 3

Repeat thousands of times.

=============================================================================

SIER.EXE requires VGA graphics and a 286 or better machine to run.
It is Freeware, and the source code is herewith placed in the Public Domain.


M\Cooper
3138 Foster Ave.
Baltimore, MD 21224