Representing Families of Cellular Automata Rules

Abstract

This article introduces the notion of a representation of cellular automata rules based on a template. This enhances the standard representation based on a rule table, in that it refers to families of cellular automata, instead of a rule alone. The key for obtaining the templates is the role of the built-in equation-solving capabilities of Mathematica. Operations applicable to the templates are defined, and examples of their use are given in the context of finding representations for rule sets that share the properties of maximum internal symmetry or number conservation. The perspectives for using templates in further contexts are also discussed and current limitations are addressed.