Notes

Chapter 11: The Notion of Computation

Section 2: Computations in Cellular Automata


[Rules for the] primes cellular automaton

The rules are

{{13, 3, 13} 12, {6, _, 4} 15, {10, _, 3 | 11} 15, {13, 7, _} 8, {13, 8, 7} 13, {15, 8, _} 1, {8, _, _} 7, {15, 1, _} 2, {_, 1, _} 1, {1, _, _} 8, {2 | 4 | 5, _, _} 13, {15, 2, _} 4, {_, 4, 8} 4, {_, 4, _} 5, {_, 5, _} 3, {15, 3, _} 12, {_, x : (2 | 3 | 8), _} x, {_, x : (11 | 12), _} x - 1, {11, _, _} 13, {13, _, 1 | 2 | 3 | 5 | 6 | 10 | 11} 15, {13, 0, 8} 15, {14, _, 6 | 10} 15, {10, 0 | 9 | 13, 6 | 10} 15, {6, _, 6} 0, {_, _, 10} 9, {6 | 10, 15, 9} 14, {_, 6 | 10, 9 | 14 | 15} 10, {_,6|10,_} 6, {6 | 10, 15, _} 13, {13 | 14, _, 9 | 15} 14, {13 | 14, _, _} 13, {_, _, 15} 15, {_, _, 9 | 14} 9, {_, _, _} 0}

and the initial conditions consist of {10, 0, 4, 8} surrounded by 0's. The right-hand region in the pattern grows like t. (See also page 132.)

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