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The formation of voronoi diagrams in chemical and physical systems: Experimental findings and theoretical models

Purwins, Hans Georg; de Lacy Costello, Ben; Ratcliffe, Norman M.; Adamatzky, Andrew; Zanin, Alexey L.; Liehr, Andreas W.


Hans Georg Purwins

Norman Ratcliffe
Professor in Materials & Sensors Science

Alexey L. Zanin

Andreas W. Liehr


The work discusses the formation of Voronoi diagrams in spatially extended nonlinear systems taking experimental and theoretical results into account. Concerning experimental systems a number of chemical systems used previously as prototype chemical processors and a barrier gas-discharge system are investigated. Although the underlying microscopic processes are very different, both types of systems show self-organized Voronoi diagrams for suitable parameters. Indeed certain chemical systems exhibit Voronoi diagrams as an output state for two distinct sets of parameters one that corresponds to the interaction of stable forced trigger waves and the other that corresponds to the spontaneous initiation and interaction of waves due to point instabilities in the system. In the case of the chemical systems front initiation, propagation and interaction (annihilation) are the primary mechanisms for Voronoi diagram formation, in the case of the barrier gas-discharge system regions of vanishing electric field define the medial axes of the Voronoi diagram. On the basis of cellular automata models the general concept of the formation of Voronoi diagrams has been explained, and related mechanisms have been simulated. Another intuitive approach towards the understanding of self-organized Voronoi diagrams has been given on the basis of reaction-diffusion models explaining the formation of Voronoi diagrams as a result of the mutual interactions of trigger fronts. The variety of systems exhibiting Voronoi diagrams as stationary states indicates that Voronoi diagrams are a generic and natural pattern formation phenomenon.


Purwins, H. G., de Lacy Costello, B., Ratcliffe, N. M., Adamatzky, A., Zanin, A. L., & Liehr, A. W. (2004). The formation of voronoi diagrams in chemical and physical systems: Experimental findings and theoretical models. International Journal of Bifurcation and Chaos, 14(7), 2187-2210.

Journal Article Type Review
Publication Date Jan 1, 2004
Journal International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Print ISSN 0218-1274
Publisher World Scientific Publishing
Peer Reviewed Peer Reviewed
Volume 14
Issue 7
Pages 2187-2210
Keywords pattern formation, reaction–diffusion, voronoi diagrams, front-propagation, front-interaction, gas discharge, barrier discharge
Public URL