The chaos game is a random-iteration method for an iterated function system. In its polygonal form, pick a point
at random inside a regular polygon with sides. 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 regular
polygons with 3, 4, 5, and 6 sides 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.
sides. 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 
.
points in regular
polygons with 3, 4, 5, and 6 sides with 
. The case 
gives the interior of a square
with all points visited with equal probability.
points in the square
with 
, 0.4, 0.5, 0.6, 0.75, and 0.9.
