Cellular automata are the simplest models of spatially distributed processes. They consist of an array of cells, each of which is allowed to be in one of a few states. At the same time, each cell looks to its neighbors to see what states they are in. Using this information each cell applies a simple rule to determine what state it should change to. This basic step is repeated over the whole array, again and again. Some of the patterns produced, by several simple cellular automata, are shown on this page.
Cellular automata were invented in the 1940's by the mathematicians John von Neuman and Stanislaw Ulam, while they were working at the Los Alamos National Laboratory in northern central New Mexico. The most famous cellular automaton is the "Game Of Life" invented by mathematician John Conway, in the 1960's. Despite the simplicity of the rules governing the changes of state as the automaton moves from one generation to the next, the evolution of such a system is complex indeed.
For interactive cellular automata simuations, go to Prof. David Griffeath's Java-based page CAffeine. (The images on this page were produced by Prof. Griffeath and his students.)
A great collection of animated simulations is available at the Live Artificial Life Page.