A cellular automaton can be thought of as a stylised universe. A cellular automata is a discrete dynamical system whose behaviour is completely specified in terms of a local relation. Space is represented by a uniform grid, with each cell containing a few bits of data; time advances in discrete steps and the laws of the "universe" are expressed in, say, a small look-up table, through which at each step each cell computes its new state from that of its close neighbours. Thus, the system's laws are local and uniform.

According to mathworld at Wolfram.com, "A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells. The rules are then applied iteratively for as many time steps as desired."

from http://www.brunel.ac.uk/depts/AI/alife/al-ca.htm
http://mathworld.wolfram.com/CellularAutomaton.html