Wave propagation in filamental cellular automata

TL;DR

This paper explores wave-like behaviors in one-dimensional cellular automata inspired by biology, identifying minimal conditions for self-stabilizing waves and examining collective behaviors through simulations.

Contribution

It determines the minimal state and communication range needed for wave propagation and analyzes collective features of growing filament populations.

Findings

Identified minimal states and communication range for wave propagation.

Discovered collective behaviors in growing filament populations.

Provided numerical simulation results illustrating these phenomena.

Abstract

Motivated by questions in biology and distributed computing, we investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata. We investigate what sort of self-stabilising cooperative behaviour these can induce in terms of waves of cellular state changes along a filament of cells. We discover what the minimum requirements are, in terms of numbers of states and the range of communication between automata, to observe this for individual filaments. We also discover that populations of growing filaments may have useful features that the individual filament does not have, and we give the results of numerical simulations.