Tessie, the Tessellation Automata
This is an interactive Tessellation Automata, as described in Dr. Cliff Pickover's excellent book, Computers, Pattern, Chaos, and Beauty.
Try it! Click around on the background to add seeds from which the lattice will grow.
What's happening? This is an example of an emergent macro pattern from a set of simple micro rules. First, We start with an empty grid. The lattice grows from an initial seed (placed randomly) on the grid. At each step during the growth of the lattice, each individual cell of the lattice (whether lit or dim) checks with its neighbors. If you're feeling adventurous, have a look at the Java sourcecode.
It's similar to Conway's game of life, but with no deaths in the system the lattice "crystalizes" into place and stays put.