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.You can have linear cellular automata,like
the one shown in the applet, planar CA and even 3D CA.
At each tick of 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.

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 . The most famous
cellular automaton is the "Game
Of Life" invented by mathematician John
Conway, in the 1960's. This is a planar CA and 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.

A spatial process is normally described by a set of PDE(Partial Differential Equations) with time,space and state
space continuous.In a Cellular Automaton time is discrete like in a map,
space is discrete (the cells of a cellular automaton) and also state
space is discrete(each cell can have only a finite number of states).
So it is the simplest dynamical system that describes systems evolving in space.

For interactive cellular automata simulations, go to Prof. David Griffeath's
Java-based page CAffeine.