Excitable Delaunay triangulations

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

Kybernetes

ISSN: 0368-492X

Publication date: 14 June 2011

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Keywords

Citation

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

Download as .RIS

Publisher

:

Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited

Please note you might not have access to this content

You may be able to access this content by login via Shibboleth, Open Athens or with your Emerald account.
If you would like to contact us about accessing this content, click the button and fill out the form.
To rent this content from Deepdyve, please click the button.