Murmurations form over winter roosts, most visibly at dusk. Researchers photographed wheeling flocks with synchronised cameras and reconstructed the positions of thousands of individual birds in three dimensions. The resulting analysis showed that a starling's motion is correlated with a roughly constant count of its nearest neighbours rather than with all birds inside a fixed radius.
The distinction matters because it makes the flock scale-free. If each bird tracked everything within, say, three metres, then a flock that spread out would fragment. Tracking a set number of neighbours instead means the coupling survives expansion and compression, which is why a turn initiated at one edge propagates across the whole flock as a visible wave.
The function is less settled than the mechanism. Anti-predator benefits against peregrines and sparrowhawks are plausible and partly supported, and roost advertisement or thermal benefit have also been proposed, but no single explanation accounts for all observed murmuration behaviour.