Notes

Chapter 11: The Notion of Computation

Section 2: Computations in Cellular Automata


[Rules for the] squaring cellular automaton

The rules are

{{0, _, 3} 0, {_, 2, 3} 3, {1, 1, 3} 4, {_, 1, 4} 4, {1 | 2, 3, _} 5,{p : (0 | 1), 4, _} 7 - p, {7, 2, 6} 3, {7, _, _} 7, {_, 7, p : (1 | 2)} p, {_, p : (5 | 6), _} 7 - p, {5 | 6, p : (1 | 2), _} 7 - p, {5 | 6, 0, 0} 1, {_, p : (1 | 2), _} p, {_, _, _} 0}

and the initial conditions consist of Append[Table[1, {n}], 3] surrounded by 0's. The rules can be implemented using GeneralCARule as given on page 867. (See also page 1186.)

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