Chapter 3: The World of Simple Programs

Section 2: More Cellular Automata

Common framework [for cellular automaton rules]

The Mathematica built-in function CellularAutomaton discussed on page 867 handles general and totalistic rules in the same framework by using ListConvolve[w, a, r + 1] and taking the weights w to be respectively k^Table[i - 1, {i, 2r + 1}] and Table[1, {2r + 1}].

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