Geometry estimation of planar swarm patterns

Phenomena of coupled individuals or particles aggregating to form cohesive patterns are ubiquitous in nature and human society. Estimation of the pattern geometry is of interest in many cases. This Letter considers a planar swarm system consisting of finite particles with long-range attractive and short-range repulsive interactions. An analytical approach is presented to evaluate the relative distance of neighboring particles and the diameter of the swarm pattern. The method is based on a scale transformation on minimum interaction potential condition of the steady state of the system, and can give conditions determining distance between neighboring particles in the steady state pattern as well as the size of it, under certain distribution assumptions. Numerical simulations are also carried out to show effectiveness of the approach.