Complex Systems

Complex Dynamics Emerging in Rule 30 with Majority MemoryDownload PDF

Genaro J. Martínez
Department of Computer Science
University of the West of England
Bristol BS16 1QY, United Kingdom
Instituto de Ciencias Nucleares and Centro de Ciencias de la Complejidad
Universidad Nacional Autónoma de México
genaro.martinez@uwe.ac.uk

Andrew Adamatzky
Department of Computer Science
University of the West of England
Bristol BS16 1QY, United Kingdom

Ramon Alonso-Sanz
Department of Computer Science
University of the West of England
Bristol BS16 1QY, United Kingdom

Juan C. Seck-Tuoh-Mora
Centro de Investigación Avanzada en Ingeniería Industrial
Universidad Autónoma del Estado de Hidalgo Pachuca
Hidalgo, México

Abstract

In cellular automata (CAs) with memory, the unchanged maps of conventional CAs are applied to cells endowed with memory of their past states in some specified interval. We implement the rule 30 automaton and show that by using the majority memory function we can transform the quasi-chaotic dynamics of classical rule 30 into domains of traveling structures with predictable behavior. We analyze morphological complexity of the automata and classify glider dynamics (particle, self-localizations) in the memory-enriched rule 30. Formal ways of encoding and classifying glider dynamics using de Bruijn diagrams, soliton reactions, and quasi-chemical representations are provided.