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A cellular automaton is a model used in computer science and mathematics. The idea is to model a dynamic system by using a number of cells. Each cell has one of many possible states. With each "turn" or iteration the state of the current cell is determined by two things: its current state, and the states of the neighbouring cells.
A very famous example of a cellular automaton is Conway's Game of Life. Stanislaw Ulam and John von Neumann first described cellular automata in the 1940s. Conway's Game of Life was first shown in the 1970s.