Pick a point at random inside a regular -gon. Then draw the next point a fraction of the distance between it and a Vertex picked at random. Continue the process (after throwing out the first few points). The result of this ``chaos game'' is sometimes, but not always, a Fractal. The case gives the interior of a Square with all points visited with equal probability.

**References**

Barnsley, M. F. and Rising, H. *Fractals Everywhere, 2nd ed.* Boston, MA: Academic Press, 1993.

Dickau, R. M. ``The Chaos Game.'' http://forum.swarthmore.edu/advanced/robertd/chaos_game.html.

Wagon, S. *Mathematica in Action.* New York: W. H. Freeman, pp. 149-163, 1991.

Weisstein, E. W. ``Fractals.'' Mathematica notebook Fractal.m.

© 1996-9

1999-05-26