Complex Systems

On Patterns and Dynamics of Rule 22 Cellular Automaton Download PDF

Genaro J. Martínez
Laboratorio de Ciencias de la Computación
Escuela Superior de Cómputo
Instituto Politécnico Nacional, México

Andrew Adamatzky
Unconventional Computing Lab
Department of Computer Science and Creative Technologies
University of the West of England
Bristol, United Kingdom

Rolf Hoffmann
Technische Universität Darmstadt
Darmstadt, Hessen, Deutschland

Dominique Désérable
Institut National des Sciences Appliquées
Rennes, France

Ivan Zelinka
Fakulta Elektrotechniky a Informatiky
Technická Univerzita Ostrava, Czechia


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.

Keywords: elementary cellular automata; rule 22; chaos and complex dynamics