Chapter 11: The Notion of Computation

Section 5: Emulating Other Systems with Cellular Automata

Mobile automata [from cellular automata]

Given a mobile automaton with rules in the form used on page 887, a cellular automaton which emulates it can be constructed using

MAToCA[rules_] := Append[Flatten[Map[g, rules]], {_, _, x_, _, _} -> x]

g[{a_, b_, c_} -> {d_, e_}] := {{_, a, b+2, c, _} -> d, If[e==1, {a, b+2, c, _, _} -> c+2, {_, _, a, b+2, c} -> a+2]}

This specific definition assumes that the mobile automaton has two possible colors for each cell; it yields a cellular automaton with four possible colors for each cell. An initial condition with a single 2 surrounded by 0's corresponds to all cells being white in the mobile automaton.

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