On patterns and dynamics of rule 22 cellular automaton

Abstract

Rule 22 elementary cellular automaton (ECA) has a three-cell neighborhood, binary cell state, where a cell takes state "1" if there is exactly one neighbor, including the cell itself, in state 1. In Boolean terms, the cell state transition is an XOR function of three cell states. In physico- chemical terms, the rule might be seen as describing propagation of self-inhibiting quantities/species. Spacetime dynamics of rule 22 demonstrate nontrivial patterns and quasi-chaotic behavior. We characterize the phenomena observed in this rule using mean field theory, attractors, de Bruijn diagrams, subset diagrams, filters, fractals and memory.