Complex Systems

A Symbolic Dynamics Perspective of the Game of Three-Dimensional Life Download PDF

Bo Chen
Fangyue Chen
Department of Mathematics, School of Science
Hangzhou Dianzi University
Hangzhou, Zhejiang, China

Genaro J. Martínez
Escuela Superior de Cómputo, Instituto Politécnico Nacional
México D. F., México
International Center of Unconventional Computing
University of the West of England
BS16 1QY Bristol, United Kingdom

Danli Tong
College of International Business
Zhejiang Yuexiu University of Foreign Languages
Shaoxing, China


The games of three-dimensional life are the extension models of Conway's Game of Life. Under the framework of symbolic dynamics, we undertake an analysis of the complexity of gliders in games of three-dimensional life rules by the directed graph representation and transition matrix. More specifically, the gliders here are topologically mixing and possess positive topological entropy on their concrete subsystems. Finally, the method presented in this paper is also applicable to other gliders in different D-dimensions.