Emergence of Collective Behaviors from Local Voronoi Topological Perception

TL;DR

This paper introduces a 2D agent-based model where individuals make decisions based solely on their local Voronoi environment, leading to diverse collective behaviors and new ways to quantify them.

Contribution

It presents a novel Voronoi-based decision model for agents, enabling the emergence of complex collective behaviors from simple local rules.

Findings

Model captures a wide range of behaviors with two parameters.

Voronoi topology helps quantify collective behaviors.

Applicable to empirical data and various models.

Abstract

This article addresses how diverse collective behaviors 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 2D 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 neighbors 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 behaviors in different scenarios. Further, we show that the Voronoi topology facilitates the computation of several novel observables for quantifying discrete collective behaviors. These observables are applicable to all agent-based models and to empirical data.