Chapter 2: The Crucial Experiment

Section 3: Why These Discoveries Were Not Made Before

Code 10

Rule 30 is by many measures the simplest cellular automaton that generates randomness from a single black initial cell. But there are other simple examples—that historically I noticed slightly earlier than rule 30, though did not study—that occur in k = 2, r = 2 totalistic rules. And indeed among the 64 such rules, 13 show randomness. An example shown below is code 10, which specifies that if 1 or 3 cells out of 5 are black then the next cell is black; otherwise it is white.

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