Spatial and temporal competition as a two dimensional kinetic Voronoi diagram

An ordinary Voronoi diagram partitions the space into cells with the assumption that all the sites are of the same characteristics. A kinetic site, in addition to its position and hence distance to other sites, is equipped with two more characteristics: an additive constant (such as the time delay to respond to a stimulus) and a multiplicative constant (such as the growth rate or velocity to “catch up”). Under disparate site characteristics, the resulting competition for space becomes unfair: the notion of dominance and conquest ensue. This article reports on the geometry and the topology of kinetic Voronoi regions as pivoted by simple expressions involving dimensionless numbers derived from the site characteristics.