Excitable Delaunay triangulations

TL;DR

This paper explores how excitable Delaunay triangulations model wave propagation phenomena, revealing complex behaviors like reflection, backfire, and localized excitation, contributing to understanding perturbations in non-crystalline structures.

Contribution

It introduces a novel model of excitable nodes on Delaunay triangulations and demonstrates diverse wave behaviors depending on node excitability.

Findings

Reflection of excitation waves from edges

Backfire of excitation waves

Formation of localized excitation domains

Abstract

In an excitable Delaunay triangulation every node takes three states (resting, excited and refractory) and updates its state in discrete time depending on a ratio of excited neighbours. All nodes update their states in parallel. By varying excitability of nodes we produce a range of phenomena, including reflection of excitation wave from edge of triangulation, backfire of excitation, branching clusters of excitation and localized excitation domains. Our findings contribute to studies of propagating perturbations and waves in non-crystalline substrates.