Excitable Delaunay Triangulations

Abstract

Given a planar finite set V the Delaunay triangulation [92] ${\mathcal D}$(V)= 〈V, E 〉 is a graph subdividing the space onto triangles with vertices in V and edges in E where the circumcircle of any triangle contains no points of V other than its vertices. Neighbours of a node v ∈ V are nodes from V connected with v by edges from E.

The set V is constructed as follows. We take a disc-container of radius 480 and fill it with up to 15,000 disc-nodes. We assume that each disc-node has radius 2.5, thus a minimal distance between any two nodes is 5. The Voronoi diagram, and its dual triangulation, are appropriate representations of such identical sphere packing on two-dimensional surface, where planar points of V represent centres of the spheres.