Flocking Boids: Emergence from Simple Rules

Craig Reynolds' 1987 boids model uses three rules: separation, alignment, cohesion. Remarkably, complex flocking emerges.

The Vicsek model (1995) simplifies to: each bird copies neighbors' average heading + noise. At low noise, the flock spontaneously orders — a phase transition in 2D.

The order parameter ψ = |⟨v̂⟩| measures flock alignment. It jumps from 0 (disordered) to 1 (fully aligned) as noise decreases — a genuine symmetry-breaking transition.

Click the canvas to add a disturbance.