  Flocking is a paradigmatic example of collective animal behaviour, where
decentralized interaction rules give rise to a globally ordered state. In the
emergence of order out of self-organization we find similarities between
biological systems, as bird flocks, and some physical systems, as ferromagnets.
In both cases, the tendency of individuals to align to their neighbours gives
rise to a polarized state. There is, however, one crucial difference: the
interaction network within an animal group is not necessarily fixed in time, as
each individual moves and may change its neighbours. Therefore, the dynamical
interaction mechanism in biological and physical system can be quite different,
not only due to the gross disparity in the complexity of the individual
entities, but also because of the potential role of inter-individual motion. To
assess the relevance of this mechanism it is necessary to gain quantitative
experimental information about how much individuals move with respect to each
other within the group. Here, by using data from field observations on
starlings, we study the diffusion properties of individual birds within a flock
and investigate the effect of diffusion on the dynamics of the interaction
network. We find that birds diffuse faster than Brownian particles
(superdiffusion) and in a strongly anisotropic way. We also find that
neighbours change in time exclusively as a consequence of diffusion, so that no
specific mechanism to keep one's neighbours seems to be enforced. Finally, we
study the diffusion properties of birds at the border of the flock. We find
that these individuals remain on the border significantly longer than what
would be expected on the basis of a purely diffusional model, suggesting that
there is a sort barrier a bird must cross to make the transition from border to
interior of the flock.
