The video above shows a flock of starlings (also known as a murmuration) fluctuating over a river in Ireland. The models of collective motion we consider here are general enough that they may be applied to a wide range of systems, but the general principles were abstracted from these often spectacular starling murmurations.
Within the last decade a large scale study of murmurations was conducted in Rome.12The three-dimensional positions and velocities of individual birds in the flocks were reconstructed using stereophotographic techniques. This data allowed a number of interesting observations to be made:
The average velocity and largest dimensions of a flock lie
mostly in a plane perpendicular to gravity. For us, this suggests that
a two-dimensional model ignoring gravity may still capture some of the
essential features of the murmuration.
The spatial orientation of the flock does not change
significantly as the flock turns. This suggests that the birds are
changing the direction of their velocity much more than their speed -
and so we might consider a fixed speed model.
The birds seem to interact only with their nearest
neighbors regardless of the density of the flock. Implementing this
flexible interaction range is the major innovation in the new model.