Classification of square lattice cellular automata

All 65 536 automata on the square lattice with nearest neighbor interactions, ignoring the central spin, were simulated. We determined which percentage of them ended up in a fixed point with all spins parallel, in other fixed points, in up-down oscillations with all spins parallel, and in other oscillations of period two. Nine tenths of the rules did not fall into these classes. We also checked for “chaos”, i.e. how does the damage spread if one line of spins is reversed: For 62 percent of the possible rules it spread over the lattice, 31 percent had the damage remaining localized but nonzero, and in 7 percent of all rules the damage healed out after some time. These simulations were done with a speed of up to 120 updates, per microsecond and Cray-XMP processor.