Patterns of Flocks of Starlings Mathematically Behave How Magnets Would Move


Starling flock

Starlings, a small to medium-sized passerine bird in the family Sturnidae, achieve extraordinary coordination in flight and they behave mathematically as metals being magnetized. A new study published its findings in the journal Proceedings of the National Academy of Sciences.

The researchers described some of the aspects of starling flockings with equations used to model avalanches. The birds’ aerial formations transcend biology and span multiple physical phenomena.


(A) snapshot of a murmuration containing 1,246 starlings and their velocities (B). Image: Bialek et al./PNAS

Murmurations of Sturnus vulgaris vulargis can be found across North America and Western Europe. Flocks in Rome are renowned for their size. The team used video cameras and software to track the trajectories of individual birds and then analyzed the flock dynamics from second to second using mathematical modeling tools.

It’s already been shown that changes in the velocity of one bird affect the whole flock. The scale-free correlation is seen in systems poised at the edge of criticality, just like snow crystals in the moments before an avalanche. The researchers looked at velocity and orientation in the flock.


The orientation changes affected seven of the bird’s closest neighbors to alter their flight. This number stayed constant regardless of the flock density, which in turn made the equations describing them topological, invariant to properties that remain after continuous deformation of the flock, rather than critical in nature.

Even without criticality, changes ripple quickly through flocks, going from 7 birds to 49, etc. In physics, the closest statistical fit for this behavior is in magnetism, and it describes when particles align with their neighbors as metals become magnetized.

Starling flocks seem to be optimized to evade predators.

Reference: “Statistical mechanics for natural flocks of birds” by William Bialek, Andrea Cavagna, Irene Giardina, Thierry Mora, Edmondo Silvestri, Massimiliano Viale and Aleksandra M. Walczak, 16 March 2012, Proceedings of the National Academy of Sciences.
DOI: 10.1073/pnas.1118633109

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