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

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 threedimensional 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.