the interior of the square fills evenly with points. However, if restrictions are placed on the choice of vertices, fractals will appear in the square. For example, if the current vertex cannot be chosen in the next iteration, this fractal appears: If the current vertex cannot be one place away (anti-clockwise) from the previously chosen vertex, this fractal appears: If the point is prevented from landing on a particular region of the square, the shape of that region will be reproduced as a fractal in other and apparently unrestricted parts of the square. Here, for example, is the fractal produced when the point cannot jump so as to land on a red Om symbol at the center of the square: Jumps other than 1/2 When the length of the jump towards a vertex or another point is not 1/2, the chaos game generates other fractals, some of them very well-known. For example, when the jump is 2/3 and the point can also jump towards the center of the square, the chaos game generates the Vicsek fractal: When the jump is 2/3 and the point can also jump towards the midpoints of the four sides, the chaos game generates the Sierpinski carpet: When the jump is 1/phi and the point is jumping at random towards one or another of the five vertices of a regular pentagon, the chaos game generates a pentagonal n-flake: See also Chaos theory External links Simulations of chaos games made with Scratch. Explanation of the chaos game at beltoforion.de. References Fractals Chaos theory