Chapter 6: Starting from Randomness

Section 6: Special Initial Conditions

Uniqueness of patterns [in cellular automata]

Starting from a particular initial condition, different rules can often yield the same pattern. The picture below shows in sorted order the configurations obtained at each successive step in the evolution of all 256 elementary cellular automata starting from a single black cell. After a large number of steps, between 94 and 105 distinct individual configurations are obtained, together with 143 distinct complete patterns. (Compare page 1186.)

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