A flock of a thousand birds has no leader — each one obeys just three local rules and the murmuration emerges. Craig Reynolds’ boids are why game crowds feel alive. Slide the cohesion (or tap) between a scattered swarm and a tight flock.
Reynolds’ boids (1986). Each agent steers by three local rules over its neighbours: SEPARATION (avoid crowding), ALIGNMENT (match average heading), COHESION (steer toward the average position). No leader, no global plan — the flock is emergent. The slider scales cohesion between a loose swarm and a tight ball; alignment is measured live as the mean-heading coherence (‖Σ v̂‖/N → 1 when all aligned). A fail-loud self-check throws unless a seeded flock's heading coherence increases over time under alignment.
Sixty 2-D boids with a fixed neighbour radius (real murmurations are 3-D with thousands and aerodynamic constraints); the weights are illustrative. The three steering rules and the coherence measure are computed exactly.