Paterson's worms

Paterson's worms is a simple rule-based simulation of the movements of a single worm on a triangular grid. The worm moves in 60 degree directions along the grid lines until he reaches a position from which he can't make a turn to a path he did not already traverse.

A colorization of the different directions a worm can travel in leads to very interesting pictures that show chaotic as well as even structures.

Wikipedia has a category of this and other celluar automatons.