Emergence of collective behaviours from local Voronoi topological perception

Abstract

This article addresses how diverse collective behaviours arise from simple and realistic decisions made entirely at the level of each agent’s personal space in the sense of the Voronoi diagram. We present a discrete-time model in two dimensions in which individual agents are aware of their local Voronoi environment and may seek static target locations. In particular, agents only communicate directly with their Voronoi neighbours and make decisions based on the geometry of their own Voronoi cells. With two effective control parameters, it is shown numerically to capture a wide range of collective behaviours in different scenarios. Further, we show that the Voronoi topology facilitates the computation of several novel observables for quantifying discrete collective behaviours. These observables are applicable to all agent-based models and to empirical data.