Chapter 12: The Principle of Computational Equivalence

Section 3: The Content of the Principle

Block occurrences [in rule 30]

The pictures below show at which step each successive block of length up to 8 first appears in evolution according to various cellular automaton rules starting from a single black cell. For rule 30, the numbers of steps needed for each block of lengths 1 through 10 to appear at least once is {1, 2, 4, 12, 22, 24, 33, 59, 69, 113}. (See also page 871.)

Image Source Notebooks:

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