Chapter 12: The Principle of Computational Equivalence

Section 10: Intelligence in the Universe

[Rules implementing] other functions

The first three pictures below show rules that yield 3n (no k = 3 rules yield 4n, 5n or n2), and the last picture 2n - 2 (corresponding to doubling with initial conditions analogous to page 639).

Image Source Notebooks:

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