Vicsek Flocking — Metric-Free Topological Model

The Vicsek model exhibits a continuous flocking transition driven by noise η. Order parameter φ = |⟨e^(iθ)⟩| → 1 for aligned flocks. The metric-free (topological) variant uses the k nearest neighbors regardless of distance — as in starling murmurations.

Parameters

Noise η 0.2 k neighbors 7 Speed v 2.0 N particles 300

Order

φ (alignment): —

⟨θ⟩ direction: —

Color = heading direction
φ=1: perfect flock
φ=0: disordered gas
Topological: k neighbors, not radius