Chapter 9: Fundamental Physics

Section 2: The Notion of Reversibility

Classification of reversible rules

In a reversible system it is possible with suitable initial conditions to get absolutely any arrangement of cells to appear at any step. Despite this, however, the overall spacetime pattern of cells is not arbitrary, but is instead determined by the underlying rules. If one starts with completely random initial conditions then class 2 and class 3 behavior are often seen. Class 1 behavior can never occur in a reversible system. Class 4 behavior can occur, as in rule 37R, but is typically obvious only if one starts say with a low density of black cells.

For arbitrary rules, difference patterns of the kind shown on page 250 can get both larger and smaller. In a reversible rule, such patterns can grow and shrink, but can never die out completely.

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