Nobody Leads — How do thousands of birds fly in one flock without crashing?

Thousands of starlings fly as a single shape without a leader and without ever crashing into each other. Each bird is following just three simple rules about its nearest few neighbours: keep some space, go the same way, do not get left behind. Switch the three rules on one at a time and watch a scatter of drifting birds turn into one animal that a falcon cannot pick a target out of - then lead the whole flock down into the reeds yourself.