Emergence of Anisotropy in Flock Simulations and Its Computational Analysis

Abstract

In real flocks, it was revealed that the angular density of nearest neighbors shows a strong anisotropic structure of individuals by very recent extensive field studies [Ballerini et al, Proceedings of the National Academy of Sciences USA, 105, pp. 1232-1237 (2008)]. In this paper, we show this structure of anisotropy also emerges in an artificial flock simulation, namely, Boid simulation. To quantify the anisotropy, we evaluate a useful statistics, that is to say, the so-called γ-value which is 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 moving of the flock. Our results concerning the emergence of the anisotropy through the γ-value might enable us to judge whether an optimal flock simulation seems to be realistic or not.