Flocking — Vicsek Polar Order

Vicsek model: each bird aligns its velocity with neighbors within radius r, plus angular noise η. Order parameter φ = |Σ v̂ᵢ|/N transitions from 1 (ordered flock) to 0 (disordered) as noise increases — a kinetic phase transition.

Noise η0.20
Interaction radius25
Speed3
N birds200
Order parameter φ = —