A flock with no leader
How thousands of birds move as one, with every bird following three simple rules.
What you are looking at
A cloud of dots swirls and folds, changing shape smoothly. It looks planned, but each dot only reacts to the dots right next to it.
The idea
Large flocks of starlings make shapes in the sky that look like they were planned. But there is no leader. Each bird follows three simple rules:
- Stay close to the birds around you.
- Fly the same way they do.
- Do not bump into anyone.
That is all. Each bird only looks at the few birds closest to it. But when thousands of birds do this at the same time, the whole flock bends, twists, and folds like one animal.
The big idea: a pattern on a large scale does not need a plan on a large scale. It can come from small, local rules.
Where else you see it
- Starling flocks (murmurations) at dusk.
- Schools of fish.
- Traffic jams and crowds, which also come from many people following simple local rules.
Go deeper: the proper names and the math
These rules are the boids model by Craig Reynolds (1986): separation, alignment, and cohesion. It was used in films to animate crowds, flocks, and swarms, starting with the bats and penguins in Batman Returns (1992).
Measurements of real starling flocks (Ballerini et al., 2008) found that each bird tracks about six or seven nearest neighbors, not all birds within a fixed distance. This keeps a flock together even when it gets stretched out or thinned. Flocks also show correlations across the whole group, so a change in one part is felt everywhere. Robot swarms use the same ideas.