On Binary-State Phyllosilicate Automata

Abstract

Phyllosilicate is a sheet of silicate tetrahedra bound by basal oxygens. A phyllosilicate automaton is a regular network of finite state machines, which mimics the structure of phyllosilicate. A node of a binary state phyllosilicate automaton takes states 0 and 1. A node updates its state in discrete time depending on a sum of states of its three (silicon nodes) or six (oxygen nodes) closest neighbors. We phenomenologically select the main types of patterns generated by phyllosilicate automata based on their shape: convex and concave hulls, almost circularly growing patterns, octagonal patterns, and those with dendritic growth; and, the patterns' interior: disordered, solid, labyrinthine. We also present the rules exhibiting traveling localizations.