The Role of Projection in the Control of Bird Flocks
Daniel J. G. Pearce, A. M. Miller, George Rowlands, Matthew, S. Turner

TL;DR
This paper proposes that bird flocks self-organize to a marginally opaque state, enabling global information exchange through visual projection, which enhances collective control and rapid response beyond local interaction models.
Contribution
It introduces the concept that flock opacity constrains interactions and facilitates global information transfer via visual projection, challenging local interaction assumptions.
Findings
Flocks self-organize to maximum density with marginal opacity.
Visual projection enables faster, global information transfer.
Flocks can be highly diffuse or opaque, but tend to be marginally opaque.
Abstract
Swarming is a conspicuous behavioural trait observed in bird flocks, fish shoals, insect swarms and mammal herds. It is thought to improve collective awareness and offer protection from predators. Many current models involve the hypothesis that information coordinating motion is exchanged between neighbors. We argue that such local interactions alone are insufficient to explain the organization of large flocks of birds and that the mechanism for the exchange of long-ranged information necessary to control their density remains unknown. We show that large flocks self-organize to the maximum density at which a typical individual is still just able to see out of the flock in many directions. Such flocks are marginally opaque - an external observer can also just still see a substantial fraction of sky through the flock. Although seemingly intuitive we show that this need not be the case;…
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