### Abstract

The convergence time for flocking in the Vicsek-Cucker-Smale model is known to be bounded by a tower-of-twos of height linear in the number of birds. We improve the height to logarithmic, which matches the known lower bound. In the process, we introduce an intriguing geometric object, the flight net, and develop the idea of a virtual agent. These two concepts give us insight into early flocking behavior, which is still the most mysterious aspect of these dynamical systems.

Original language | English (US) |
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Title of host publication | Proceedings of the 26th Annual Symposium on Computational Geometry, SCG'10 |

Pages | 19-28 |

Number of pages | 10 |

DOIs | |

State | Published - Jul 30 2010 |

Event | 26th Annual Symposium on Computational Geometry, SoCG 2010 - Snowbird, UT, United States Duration: Jun 13 2010 → Jun 16 2010 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
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### Other

Other | 26th Annual Symposium on Computational Geometry, SoCG 2010 |
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Country | United States |

City | Snowbird, UT |

Period | 6/13/10 → 6/16/10 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

### Keywords

- Bird flocking
- Flight net
- Multiagent agreement systems

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## Cite this

Chazelle, B. (2010). The geometry of flocking. In

*Proceedings of the 26th Annual Symposium on Computational Geometry, SCG'10*(pp. 19-28). (Proceedings of the Annual Symposium on Computational Geometry). https://doi.org/10.1145/1810959.1810963