Game of Life on Phyllosilicates: Gliders, Oscillators and Still Life

Abstract

A phyllosilicate is a sheet of silicate tetrahedra bound by basal oxygens. A phyllosilicate automaton is a regular network of finite state machines --- silicon nodes and oxygen nodes --- which mimics structure of the phyllosilicate. A node takes states 0 and 1. Each node updates its state in discrete time depending on a sum of states of its three (silicon) or six (oxygen) neighbours. Phyllosilicate automata exhibit localizations attributed to Conway's Game of Life: gliders, oscillators, still lifes, and a glider gun. Configurations and behaviour of typical localizations, and interactions between the localizations are illustrated.