Chapter 9: Fundamental Physics

Section 2: The Notion of Reversibility

Properties [of second-order cellular automata]

The pattern from rule 67R with simple initial conditions grows irregularly, at an average rate of about 1 cell every 5 steps. The right-hand side of the pattern from rule 173R consists three triangles that repeat progressively larger at steps of the form 2 (9^s-1). Rule 90R has the property that of the diamond of cells at relative positions {{-n,0},{0,-n},{n,0},{0,n}} it is always true for any n that an even number are black.

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