The equations that describe these movements are equivalent to those that govern waves.
Cavagna was hardly the first scientist to be intrigued by these acrobatics—known, in a rare instance of technical language coinciding with poetry, as “murmurations.” Other animals that travel in groups—schooling fish, most obviously—show the same uncanny ability to move in apparent unison away from a predator or toward a food source. One 20th-century ornithologist seriously proposed that they coordinated their movements by telepathy. That possibility hasn’t found much support in biology. The other explanation is that a signal to change direction originates with one or a few individuals, probably on the periphery (the ones most likely to see a threat), and travels as a wave front across the flock, like a ripple spreading across a pond from a dropped pebble. It is just an artifact of human vision that we can’t see it happen in real time. But high-speed cameras can capture it, and computers can model the behavior.