Vicsek Flocking Model
Alignment, noise, and the order-disorder transition in self-propelled particles
Controls
Noise η
0.30
Interaction radius r
0.10
Speed v
0.03
N particles
200
Reset Particles
Order Parameter
φ = 0.00
Phase: —
Initializing…
Physics
Vicsek model (1995)
: N particles move with constant speed v. Each updates heading to the mean angle of neighbors within radius r, plus noise η.
Order parameter
: φ = |⟨e^{iθ}⟩| ∈ [0,1]
φ≈1 → ordered flock; φ≈0 → disordered gas. Critical noise η_c separates phases — a
continuous phase transition
.