Local Structure Theory

Local Structure Theory: Calculation on Hexagonal Arrays, and Interaction of Rule and Lattice

Howard A. Gutowitz and Jonathan D. Victor

Journal of Statistical Physics, 54, 495-514 (1989)

Abstract

Local structure theory calculations are applied to the study of cellular automata on the two-dimensional hexagonal lattice. A particular hexagonal lattice rule denoted (3422) is considered in detail. This rule has many features in common with Conway's Life. The local structure theory captures many of the statistical properties of this rule; this supports hypotheses raised by study of Life itself. As in Life, the state of a cell under (3422) depends only on the state of the cell itself and the sum of states in its neighborhood at the previous time step. This property implies that evolution rules which opeate in the same way can be studied on different lattices are dramatic. This mean field theory cannot reflect these differences. However, a generalization of the mean field theory, the local structure theory, does account for the rule-lattice interaction.

Download