On oscillators in phyllosilicate excitable automata

TL;DR

This paper investigates the behavior of excitable automata modeled after phyllosilicate sheets, demonstrating phenomena like spiral waves, oscillators, and wave dynamics, and classifying oscillator types.

Contribution

It introduces a novel automaton model based on phyllosilicate structure and classifies various oscillator configurations within this framework.

Findings

Exhibits spiral and target wave patterns

Identifies and classifies oscillator types

Demonstrates localized oscillating dynamics

Abstract

Phyllosilicate is a sheet of silicate tetrahedra bound by basal oxygens. A phyllosilicate excitable automaton is a regular network of finite state machines, which mimics structure of a silicate sheet. A node of the silicate sheet is an automaton, which takes resting, excited and refractory states, and updates its state in discrete time depending on a sum of excited states of its three (silicon automata) or six (oxygen automata) closest neighbours. Oscillator is a localised compact configuration of non-quiescent states which undergoes finite growth and modification but returns to its original state in a finite number of steps. We show that phyllosilicate excitable automata exhibit spiral and target waves, and oscillating localisation dynamics. Basic types of oscillators are classified and characterised.