Chapter 5: Two Dimensions and Beyond

Section 2: Cellular Automata

Growth [2D cellular automaton] rules

The pictures below show examples of rules in which a cell becomes black if it has exactly the specified numbers of black neighbors (the initial conditions used have the minimal number of black cells for growth). The code numbers in these cases are given by 2 (4^n - 1)/3 + Apply[Plus, 4^list] where n is the number of neighbors, here 5. (See also the 9-neighbor examples on page 373.)

From Stephen Wolfram: A New Kind of Science [citation]