Vicsek Flocking Model

Collective motion and the order-disorder phase transition in active matter

Noise η 0.50

Particles N 200

Speed v 1.50

Radius r 30

Action

Order φ: —

Time: 0

Density ρ: —

Vicsek model (1995): each particle moves at constant speed, aligning with neighbors within radius r, plus angular noise η. Below the critical noise η_c, order parameter φ=|Σvᵢ|/Nv → 1 (collective motion). Above η_c, φ→0 (disorder). This is a continuous non-equilibrium phase transition. Color encodes heading direction (hue = angle).