Totalistic

BTW: Of course the rules were parametrised, so any totalistic 2-dimensional 9-neighbourhood CA could be run.

Note that the game of life is not totalistic: the transition function depends on the cell's own state and on the sum of the neighboring states.

The Xor operation drastically cuts down the number of operations when dealing with totalistic CA rules. For example, a function of four variables a, b, c, d, returning 1 iff there are exactly two ones and two zeros among its arguments, is represented by this Karnaugh diagram:

Many good applets run Moore binary totalistic rules such as Conway's Life, but WebsideCA also runs von Neumann rules, rules in the "Brian's Brain" family, non-totalistic binary and decay rules, and Cyclic rules.

Since Life is totalistic on 8 neighbours, this requires no extra assumptions.

... but the B/S notation is _the_ standard for two-state totalistic rules.