Fractals
This is an image of the first four iterations of the Koch snowflake fractal. With each iteration a smaller triangle is placed in the middle of each straight line. Theoretically one could continue such iterations indefinitely. By following this relatively simple set of rules one is able to create an extremely complex shape. Here is an example of a much more complicated fractal that has gone through many iterations:
I have put this up here to point out the similarity between fractals and repetition used in many works of Islamic art. If one looks at the image of the ceiling in the previous post you can easily see the elegant yet extremely complex touch of fractal-like patterns.