An Introduction To Artificial Life
Moshe Sipper · 1995
To conduct a formal investigation of the issue, von Neumann used a model conceived by his colleague, the mathematician Stanislaw Ulam. The model, called Cellular Automata, consists of a large grid of cells (similar to a chess board), each possessing a certain color at a given moment (every color represents a specific state). All cells change colors simultaneously such that the color of a cell at the next time step depends only on its color at the current time step and the colors of its four immediate neighbors (north, south, east, and west). The principle that guides color transformations is applied identically to all cells and is referred to as the rule. For example, a simple rule for a two-color (black/white) grid sets the color of a cell at the next time step to black if it has an even number of black neighbors, and white if it has an odd number of black neighbors.