Topological Conjugacy Classification of Two-Dimensional Cellular Automata

Abstract

This paper proposes the topological conjugacy classification of two-dimensional binary cellular automata (2D CA) with von Neumann neighborhood. By exploiting four fundamental homeomorphisms in two-dimensional symbolic sequence space, it actually partitions the global mappings, not only of the additive rules, but also of all rules, in the sense that different mappings in the same global equivalence are mutually topologically conjugate. Such classification makes it available to directly compute equivalent rules for a given rule.