Chaos game is a mechanism for generating an approximation of a fractal. You determine the vertices of a polygon, and then randomly generate a point inside of that polygon.
For an arbitrary number of steps, you move the point halfway between its current location and a randomly chosen vertex. That point is colored in, and you repeat the process as much as desired. Some chaos games, known as restricted chaos games, have requirements for a randomly chosen vertex's relation to the previous one.
If you want to make chaos games with custom shapes, go here.
Click on a square to begin the chaos game for that pattern, and click on it again to stop it.
The fractal that this approaches is the Sierpinski Triangle, which has a cleaner render here.
If the chaos game is played with a square with no rules, the entire space will be filled up. For a meaningful fractal to be established, rules must be set.