Murmuration
Three rules, no leader, and a few hundred birds self-organize into a swirling cloud. Move your cursor in to become the falcon. Three dials tune whether they flock, school, swarm, or dissolve.
avoid the too-close
steer like your neighbors
drift toward the center
This is the classical regime. Order is 80% — most birds flying the same direction — and the flock is spread over 150px, large enough that no single bird can see more than a tiny fraction of the others, yet the cloud moves as one body. The mechanism is the same as in every real murmuration ever measured: alignment propagates through nearest-neighbor chains, creating a correlation length far larger than any individual's range of perception. Drop cohesion below half a unit and the cloud will slowly dissolve. Drop separation below a unit and the birds will collapse into a tight spinning ball.
Tip: start on Murmuration, move your cursor in as the falcon and watch the cloud pour around you, then switch to Fish School and feel how the same three rules make a completely different body.
The reframe
Watch the cloud for a few seconds and notice that you cannot pick the leader. There is not one. Every bird is a follower of its handful of neighbors, and every bird is a leader for the handful watching it. The shape you see — that single, self-healing, flowing body — is not decided anywhere. It falls out of three cheap rules applied locally by every bird at every tick. Nobody designed the shape, nobody holds it together, and nobody is trying to produce it.
The STARFLAG project (Rome, 2006) photographed real starling murmurations from six synchronized cameras, tracked thousands of individual birds in three dimensions, and found that each starling responds to its seven topologically nearest neighbors, not the birds within a fixed distance. That is what the toggle above switches. In metric mode, a bird that drifts to the fringe of the flock loses connection and the cloud starts to leak. In topological mode each bird always has exactly seven contacts regardless of how the cloud stretches or compresses, so the alarm signal from a predator propagates without gaps at roughly 20 to 40 body-lengths per second.
The same principle, different medium: the polarization wave that runs through a fish school is not a message passed fish-to-fish; it is a mechanical disturbance in the pressure wave each fish creates, sensed by the lateral line of its neighbors. A wildebeest stampede does not have a signal, it has a threshold each animal crosses when enough of its neighbors are running. A stock market crash is a flock obeying fear instead of velocity. Coordination at scale nearly always turns out to be this: local rules, no global plan, and the shape falls out.
The history
Craig Reynolds, a computer animator at Symbolics, published "Flocks, Herds and Schools: A Distributed Behavioral Model" at SIGGRAPH 1987. He wanted to simulate a flock for a film sequence without choreographing every bird. The three rules — separation, alignment, cohesion — were enough, and the resulting simulations moved with a realism that stunned the audience. Reynolds called the agents "boids." Tamas Vicsek formalized a statistical-physics version in 1995 (the Vicsek model) and showed the flock undergoes a phase transition: below an alignment threshold the cloud is disordered; above it the whole group moves as one body with long-range correlations, like a ferromagnet snapping into place. The STARFLAG experiment (Ballerini et al., Nature 2008) settled the topological-vs-metric debate for real starlings. Iain Couzin (Princeton) extended the framework to collective decision-making: a tiny informed minority (1–5%) can steer a large group without revealing their source, provided cohesion is strong enough. Today the same three-rule framework, extended with noise and obstacles, is used to design swarm robotics, model evacuation flows, and describe markets.