Vesicle computers: Approximating a Voronoi diagram using Voronoi automata

Adamatzky, Andrew; De Lacy Costello, Ben; Holley, Julian; Gorecki, Jerzy; Bull, Larry

Abstract

Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata - finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one neighbour in an excited state. The cell precipitates if the ratio of excited cells in its neighbourhood versus the number of neighbours exceeds a certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto the automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate at the points of interaction. The configuration of the precipitate represents the edges of an approximated Voronoi diagram. We discover the relationship between the quality of the Voronoi diagram approximation and the precipitation threshold, and demonstrate the feasibility of our model in approximating Voronoi diagrams of arbitrary-shaped objects and in constructing a skeleton of a planar shape. © 2011 Elsevier Ltd. All rights reserved.

• Journal Article Type: Article
• Publication Date: Jul 1, 2011
• Journal: Chaos, Solitons and Fractals
• Print ISSN: 0960-0779
• Publisher: Elsevier
• Peer Reviewed: Not Peer Reviewed
• Volume: 44
• Issue: 7
• Pages: 480-489
• DOI: https://doi.org/10.1016/j.chaos.2011.01.016
• Keywords: vesicle computers, Voronoi diagram, voronoi automata
• Public URL: https://uwe-repository.worktribe.com/output/966549
• Publisher URL: http://dx.doi.org/10.1016/j.chaos.2011.01.016