A simple nearest-neighbor flocking rule

The original flocking model proposed and simulated by Reynolds [1987] and recently analytically verified to be convergent in a modified form by Tanner et. al. demands tracking and combining the movement parameters of a potentially large number of neighboring agents. We investigate an alternative simplification of the verified model wherein only two nearest neighbors are taken into account in a way that minimally preserves the convergence properties. We find that this choice also simplifies the geometry of the converged state from an amorphous distribution to a line. We speculate that this method might serve as the basis for forming more structured equilibrium distributions.