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Vesicle computers: Approximating a Voronoi diagram using Voronoi automata

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

Authors

Julian Holley julian2.holley@uwe.ac.uk

Jerzy Gorecki

Lawrence Bull Larry.Bull@uwe.ac.uk
AHOD Research and Scholarship and Prof



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Peer Reviewed Not Peer Reviewed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
APA6 Citation Adamatzky, A., De Lacy Costello, B., Holley, J., Gorecki, J., & Bull, L. (2011). Vesicle computers: Approximating a Voronoi diagram using Voronoi automata. Chaos, Solitons and Fractals, 44(7), 480-489. https://doi.org/10.1016/j.chaos.2011.01.016
DOI https://doi.org/10.1016/j.chaos.2011.01.016
Keywords vesicle computers, Voronoi diagram, voronoi automata
Publisher URL http://dx.doi.org/10.1016/j.chaos.2011.01.016