Who each bird follows
Slow-motion footage of real flocks shows there is no bird or signal steering the group. Each starling tracks its six or seven nearest neighbours, however near or far they are, and matches their heading. Drag the neighbour count down to 1 or 2 and the flock falls apart into strands; push it past 15 and the shape turns stiff and blobby.
Why the falcon matters
The tightest and most elaborate shapes appear when a predator such as a Peregrine Falcon is close. A bird on the edge or alone is an easy target, so every starling packs in toward its neighbours, and when part of the flock veers away the rest follow.
A wave, not a command
The whole flock seems to turn at once, but the turn actually passes from bird to bird so fast it crosses thousands of them in a fraction of a second. When separate parts of the flock turn different ways at the same time, the folds and ribbons you see here appear.
How this model works: each bird finds its k nearest neighbours in 3D, steers toward their average heading and position, and keeps a small gap from them. Birds close to the falcon are startled, and the startle passes neighbour to neighbour, fading a little at each step. The dark folds are just places where you see the sheet of birds edge-on. A simplified sketch, not a research model.