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COMPUTING SCIENCE

Flights of Fancy

How birds (and bird-watchers) compute the behavior of a flock on the wing

Brian Hayes

Scale-Free Flocking

Of all the findings announced so far, the most intriguing have come from a study of correlations in velocity. The existence of strong correlations is hardly a surprise. After all, if the birds weren’t all flying in roughly the same direction, the flock would disintegrate. But the result is stronger than this. Subtracting the flock’s mean velocity from each bird’s individual velocity vector leaves a field of residual fluctuations—new, smaller vectors that represent the discrepancy between each bird’s motion and the average. It turns out that these vectors too are strongly correlated.

The statistic called the correlation length is the distance beyond which one bird’s influence on another fades away, so that the two birds fly independently. Remarkably, the correlation length in starling flocks grows along with the flock itself, so that even birds at opposite ends remain connected. The correlations are said to be “scale-free.”

What’s unusual about this situation is not just that the correlation length is greater than the interaction distance. That happens in many systems. An example from physics is a ferromagnet, in which short-range interactions between atoms produce alignments over much larger distances. But the correlation length in the magnet is not scale-free; a ferromagnet of macroscopic size breaks up into many independent domains.

Why isn’t there a similar limit on the correlation length in bird flocks? One possibility is that the flock operates at a “critical point,” a set of circumstances where fluctuations extend to all possible scales of length. For a ferromagnet the critical point is a temperature known as the Curie point. In the case of bird flocks it’s not clear what would correspond to the Curie point, or even what variable would play the role of temperature. The Cavagna group explains:

Scale-free correlations imply that the group is, in a strict sense, different from and more than the sum of its parts. The effective perception range of each individual is as large as the entire group and it becomes possible to transfer undamped information to all animals, no matter their distance, making the group respond as one.

In this passage I hear an echo of Selous’s “collective thinking.” Of course no telepathy is implied; the birds communicate by ordinary physical means. And yet the outcome seems all the more impressive—and perhaps even more mysterious—for that very reason.

©Brian Hayes

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