The Convergence of Bird Flocking



May 26, 2009






Cornell University


Computer Science - Computational Geometry F.2.0

Cite this document

Bernard Chazelle, « The Convergence of Bird Flocking », arXiv, ID : 10670/1.lpkvno


Share / Export

Abstract 0

We bound the time it takes for a group of birds to reach steady state in a standard flocking model. We prove that (i) within single exponential time fragmentation ceases and each bird settles on a fixed flying direction; (ii) the flocking network converges only after a number of steps that is an iterated exponential of height logarithmic in the number of birds. We also prove the highly surprising result that this bound is optimal. The model directs the birds to adjust their velocities repeatedly by averaging them with their neighbors within a fixed radius. The model is deterministic, but we show that it can tolerate a reasonable amount of stochastic or even adversarial noise. Our methods are highly general and we speculate that the results extend to a wider class of models based on undirected flocking networks, whether defined metrically or topologically. This work introduces new techniques of broader interest, including the "flight net," the "iterated spectral shift," and a certain "residue-clearing" argument in circuit complexity.

document thumbnail

From the same authors

On the same subjects

Within the same disciplines

Export in