What is a Cellular Automata?

    Think of a series of points, each in some state.  Each point can only be in one of finite number of states -- the classic example is with two states, on/off or binary 0/1.  Based on their states, and the states of their neighbors, these points change over time.  The way the states change is often called the rule.  One key thing about Cellular Automata is that the same rule is applied to all points.  So if two points have the same states, and the configuration of their neighbors is exactly the same, than the rule should change both of them in exactly the same way; in the next time frame, these two points will be in the same state.
    1-D Cellular Automata are often graphed visually, like this:

    In these examples, imagine time = 0 at the top of the graph.  As time goes by, move down the graph, to see how the Cellular Automata evolves over time.
    The three graphs above all start the same way -- a signal dot in the very center.  However, they all have very different behavior.  This is because different rules have been applied to them.  As you can see, the rule determines the behavior of the Cellular Automata.  The same goes for multi-dimensional Cellular Automata and Cellular Automatas that allow more than just 2 states.

    There are lots of really good descriptions and analysis of Cellular Automatas out there -- this is just a very brief overview.  If you're looking for more info on Cellular Automatas, a good starting point would be Nadia's Cellular Automata page.