Stereometric photographs Clever algorithms + serious computing power Starling flocks3-D reconstruction of starling flocks

 Couzin model (and many others is metric  Topological distance is rank order Metric vs. topological difference… what’s that?

Nearest neighbor 10 th nearest neighbor v

 n c = interaction range where  (n) falls to 1/3  Anisotropy factor  tells you how non-uniform the spatial distribution of birds is.  Measures the direction of minimal crowding ( W ) relative to flock velocity ( V ) averaged over all birds  For isotropic case ncnc

Slope of this line = Sparseness for clock Slope of this line = Sparseness for clock r ~ r 1 n 1/3

 Start with:  1. Metric: r c = constant  2. Topological: n c = constant r c ~ r 1 n c 1/3 n c -1/3 ~ r 1 r c ~ r 1

Survey says… only topological hypothesis supported

 Ballerini et al. Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, PNAS, vol. 105 no. 4, 2008,  