Starling Murmuration
Topological interaction model — scale-free correlations & criticality
Flock Parameters
Birds N:
200
Topological k (neighbors):
7
Alignment strength:
0.40
Cohesion:
0.10
Noise η:
0.15
Add Predator
Flock Stats
Order φ:
—
Polarization:
—
Corr. length ξ:
—
Key Facts
Topological: each bird tracks k nearest regardless of distance (k≈7)
Scale-free: ξ/L → const as N→∞ (Cavagna 2010)
Critical point: maximum susceptibility χ = N(⟨φ²⟩−⟨φ⟩²)
Velocity correlation: C(r) = ⟨δv(0)·δv(r)⟩/⟨|δv|²⟩