Numerical study on the emergence of anisotropy in artificial flocks: A BOIDS modeling and simulations of empirical findings

TL;DR

This study demonstrates that artificial flock models based on BOIDS can reproduce the anisotropic neighbor distribution observed in real bird flocks, highlighting the role of simple interaction rules in self-organized collective behavior.

Contribution

The paper shows that specific combinations of BOIDS parameters lead to realistic anisotropic structures, providing insight into self-organization in flocking behavior.

Findings

Proper BOIDS parameters produce anisotropic neighbor distributions.

The $oldsymbol{ extgamma}$-value quantifies anisotropy and can assess simulation realism.

Artificial flocks can mimic empirical anisotropic structures observed in nature.

Abstract

In real flocks, it was revealed that the angular density of nearest neighbors shows a strong {\it anisotropic structure} of individuals by very recent extensive field studies by Ballerini et al [{\it Proceedings of the National Academy of Sciences USA} {\bf 105}, pp.1232-1237 (2008)]. In this paper, we show that this empirical evidence in real flocks, namely, the structure of anisotropy also emerges in an artificial flock simulation based on the {\it BOIDS} by Reynolds [{\it Computer Graphics} {\bf 21}, pp.25-34 (1987)]. We numerically find that appropriate combinations of the weights for just only three essential factors of the BOIDS, namely, `Cohesion', `Alignment' and `Separation' lead to a strong anisotropy in the flock. This result seems to be highly counter-intuitive and also provides a justification of the hypothesis that the anisotropy emerges as a result of self-organization of interacting intelligent agents (birds for instance). To quantify the anisotropy, we evaluate a useful statistics (a kind of {\it order parameters} in statistical physics), that is to say, the so-called $\gamma$-value defined as an inner product between the vector in the direction of the lowest angular density of flocks and the vector in the direction of the moving of the flock. Our results concerning the emergence of the anisotropy through the $\gamma$-value might enable us to judge whether an arbitrary flock simulation seems to be {\it realistic} or not.