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 Sqrt[t]. (See also page 132.)

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