Complex Systems

On Soliton Collisions between Localizations in Complex Elementary Cellular Automata: Rules 54 and 110 and Beyond Download PDF

Genaro J. Martínez
Departamento de Ciencias e Ingeniería de la Computación
Escuela Superior de Cómputo, Instituto Politécnico Nacional, México
and
Unconventional Computing Center, Bristol Institute of Technology
University of the West of England, Bristol BS16 1QY, United Kingdom
genaro.martinez@uwe.ac.uk

Andrew Adamatzky
Unconventional Computing Center, Bristol Institute of Technology
University of the West of England, Bristol BS16 1QY, United Kingdom
andrew.adamatzky@uwe.ac.uk

Fangyue Chen
School of Sciences, Hangzhou Dianzi University
Hangzhou, Zhejiang 310018, P. R. China
fychen@hdu.edu.cn

Leon Chua
Electrical Engineering and Computer Sciences Department
University of California at Berkeley, California, United States of America
chua@eecs.berkeley.edu

Abstract

In this paper, a single-soliton two-component cellular automaton (CA) model of waves is presented as mobile self-localizations, also known as particles, waves, or gliders, in addition to its version with memory. The model is based on coding sets of strings where each chain represents a unique mobile self-localization. The original soliton models in CAs proposed with filter automata are briefly discussed, followed by solutions in elementary CAs (ECAs) domain with the famous universal ECA rule 110, and reporting a number of new solitonic collisions in ECA rule 54. A mobile self-localization in this study is equivalent to a single soliton because the collisions of the mobile self-localizations studied in this paper satisfy the property of solitonic collisions. A specific ECA with memory (ECAM), the ECAM rule ØR9maj:4, is also presented; it displays single-soliton solutions from any initial codification (including random initial conditions) for a kind of mobile self-localization because such an automaton is able to adjust any initial condition to soliton structures.