Excitable Delaunay triangulations

Andrew Adamatzky (University of the West of England, Bristol, UK)


ISSN: 0368-492X

Publication date: 14 June 2011



Delaunay triangulations provide a good alternative to existing approaches of modelling unstructured unconventional computers. Experimental research in novel and emerging computing paradigms and materials shows a great progress in designing laboratory prototypes of spatially extended computing devices. In these devices, computation is implemented by excitation waves and localisations in reaction‐diffusion chemical media, geometrically constrained and compartmentalized excitable substrates, organic molecular assemblies, and gas‐discharge systems. These unconventional computing substrates can be formally represented by Delaunay triangulations with excitable nodes. Thus, it is important to uncover most common types of excitation dynamics on the Delaunay diagrams. The purpose of this paper is to define excitable automata on Delaunay triangulation and demonstrate how to control a space‐time dynamics of excitation on the triangulation using absolute and relative excitability thresholds.


The paper modifies classical Greenberg‐Hasting model to topology of Delaunay triangulations and considers not only a threshold of excitation but also a ratio of excited neighbours as an essential factor of nodes' activation. Delaunay triangulations for various densities of nodes packaging are considered.


The paper defines excitable automata on Delaunay triangulation and demonstrates how to control a space‐time dynamics of excitation on the triangulation using absolute and relative excitability thresholds. The paper uncovers several interesting phenomena ranging from reaction of excitation waves by edge of triangulation to branching domains of activity guided by travelling localized excitations.


The findings reported in the paper will contribute towards designs of novel computing substrates in non‐crystalline structure. Also, automaton interpretation of activity dynamics on Delaunay triangulation can make a viable model of automaton‐network approaches to design of nano‐computing devices.



Adamatzky, A. (2011), "Excitable Delaunay triangulations", Kybernetes, Vol. 40 No. 5/6, pp. 719-735. https://doi.org/10.1108/03684921111142278

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