Computer Science – Computational Geometry
Scientific paper
2009-05-26
Computer Science
Computational Geometry
Scientific paper
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.
No associations
LandOfFree
The Convergence of Bird Flocking does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Convergence of Bird Flocking, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Convergence of Bird Flocking will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-647508