Chapter 6: Starting from Randomness

Section 5: Randomness in Class 3 Systems

Densities in other [cellular automaton] rules

The pictures below show how the densities on successive steps depend on the initial density. Densities are indicated by gray levels. Initial densities are shown across each picture. Successive steps are shown down the page. Rule 236 is class 2, and the density retains a memory of its initial value. But in the class 3 rules 126 and 30, the densities converge quickly to a fixed value. Page 339 shows a cellular automaton with very different behavior.

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