In the post about Koch curves, I talked about how a grammar-rewrite system could be used to describe fractals. There’s a bit more to the grammar idea that I originally suggested. There’s something called an L-system (short for Lindenmayer system, after Aristid Lindenmayer, who invented it for describing the growth patterns of plants), which is a variant of the Thue grammar, which is extremely useful for generating a wide range of interesting fractals for describing plant growth, turbulence patterns, and lots of other things.