Chapter 5: Two Dimensions and Beyond

Section 2: Cellular Automata

History [of 2D cellular automata]

As indicated on pages 876-878, 2D cellular automata were historically studied more extensively than 1D ones—though rarely with simple initial conditions. The 5-cell neighborhood on page 170 was considered by John von Neumann in 1952; the 9-cell one on page 177 by Edward Moore in 1962. (Both are also common in finite difference approximations in numerical analysis.) (The 7-cell hexagonal neighborhood of page 369 was considered for image processing purposes by Marcel Golay in 1959.) Ever since the invention of the Game of Life around 1970 a remarkable number of hardware and software simulators have been built to watch its evolution. But until after my work in the 1980s simulators for more general 2D cellular automata were rare. A sequence of hardware simulators were nevertheless built starting in the mid-1970s by Tommaso Toffoli and later Norman Margolus. And as mentioned on page 1077, going back to the 1950s some image processing systems have been based on particular families of 2D cellular automaton rules.

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