An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular -gon. Then draw the next point a fraction of the distance between it and a polygon 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 results of the chaos game are shown above for several values of .

The above plots show the chaos game for points in the regular 3-, 4-, 5-, and 6-gons with . The case gives the interior of a square with all points visited with equal probability.

The above plots show the chaos game for points in the square with , 0.4, 0.5, 0.6, 0.75, and 0.9.