Vicsek Model
Parameters
Noise η:
0.2
Interaction radius r:
50
Speed v₀:
2.0
Density ρ:
0.3
N particles:
200
Reset
Toggle High Noise
Order Parameter
φ = |⟨v⟩|/v₀
—
η_c (critical noise)
—
Mean neighbors
—
Phase
—
θᵢ(t+1) = ⟨θ(t)⟩_r + ξ
ξ ~ Uniform[−ηπ, ηπ]
φ = (1/Nv₀)|Σvᵢ|
η_c ~ ρ^(1/2) (mean-field)
Phase transition at η_c: ordered→disordered
Particle Simulation
Order φ(t)
Phase Diagram ρ vs η