Mathematician Stanislaw M. Ulam liked to invent pattern games for the computer at Los Alamos. Given certain fixed rules, the computer would print out ever-changing patterns. Many patterns grew almost as if they were alive. A simple square would evolve into a delicate, coral-like growth. Two patterns would "fight" over territory, sometimes leading to mutual annihilation. He developed 3-D games too, constructing thickets of coloured cubes as prescribed by computer. He called the patterns "recursively defined geometric objects". Ulam's games were cellular games. Each pattern was composed of square (or triangular or hexagonal) cells. In effect, the games were played on limitless chessboards. All growth and change of patterns took place in discrete jumps. From moment to moment, the fate of a given cell depended only on the states of its neighbouring cells.

The advantage of the cellular structure is that it allows a much simpler physics. Without the cellular structure, there would be infinitely many possible connections between components.

Ulam suggested that John von Neumann "construct" an abstract universe for his analysis of machine reproduction. It would be an imaginary world with self-consistent rules, as in Ulam's computer games. It would be a world complex enough to embrace all the essentials of machine operation, but otherwise as simple as possible. Von Neumann adopted an infinite chessboard as his universe. Each square cell could be in any of a number of states corresponding roughly to machine components. A "machine" was a pattern of such cells.The rules governing the world would be a simplified physics. A proof of machine reproduction would be easier to devise in such an imaginary world, as all the nonessential points of engineering would be stripped away.

The first cellular automaton was conceived by Von Neumann in the late forties. [Von Neumann's work on self-reproducing automata was completed and described by Arthur Burks. In the same environment, (the Logic of Computers Group of the University of Michigan), John Holland started applying cellular automata to problems of adaptation and optimisation, and a general-purpose cellular automata simulator program was developed.]

In cellular automata, objects that may be interpreted as passive data and objects that may be interpreted as computing devices are both assembled out of the same kind of structural elements, and subject to the same laws; computation and construction are just two possible modes of activity.