  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.
