On Patterns and Dynamics of Rule 22 Cellular Automaton
Genaro J. Martínez
Laboratorio de Ciencias de la Computación
Escuela Superior de Cómputo
Instituto Politécnico Nacional, México
genaro.martinez@uwe.ac.uk
Andrew Adamatzky
Unconventional Computing Lab
Department of Computer Science and Creative Technologies
University of the West of England
Bristol, United Kingdom
andrew.adamatzky@uwe.ac.uk
Rolf Hoffmann
Technische Universität Darmstadt
Darmstadt, Hessen, Deutschland
hoffmann@informatik.tu-darmstadt.de
Dominique Désérable
Institut National des Sciences Appliquées
Rennes, France
domidese@gmail.com
Ivan Zelinka
Fakulta Elektrotechniky a Informatiky
Technická Univerzita Ostrava, Czechia
ivan.zelinka@vsb.cz
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.
Keywords: elementary cellular automata; rule 22; chaos and complex dynamics
