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In real flocks, it was revealed that the angular density of nearest neighborsshows a strong {\it anisotropic structure} of individuals by very recentextensive field studies by Ballerini et al [{\it Proceedings of the NationalAcademy of Sciences USA} {\bf 105}, pp.1232-1237 (2008)]. In this paper, weshow that this empirical evidence in real flocks, namely, the structure ofanisotropy also emerges in an artificial flock simulation based on the {\itBOIDS} by Reynolds [{\it Computer Graphics} {\bf 21}, pp.25-34 (1987)]. Wenumerically find that appropriate combinations of the weights for just onlythree essential factors of the BOIDS, namely, `Cohesion', `Alignment' and`Separation' lead to a strong anisotropy in the flock. This result seems to behighly counter-intuitive and also provides a justification of the hypothesisthat the anisotropy emerges as a result of self-organization of interactingintelligent agents (birds for instance). To quantify the anisotropy, weevaluate a useful statistics (a kind of {\it order parameters} in statisticalphysics), that is to say, the so-called $\gamma$-value defined as an innerproduct between the vector in the direction of the lowest angular density offlocks and the vector in the direction of the moving of the flock. Our resultsconcerning the emergence of the anisotropy through the $\gamma$-value mightenable us to judge whether an arbitrary flock simulation seems to be {\itrealistic} or not.

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