Topological Flocking | Voronoi Neighborhoods

Metric-free flocking where each agent aligns with its topological (Voronoi) neighbors — replicating starling murmurations.

Agents 200 Noise η 0.15 Speed 1.5 Voronoi neighbors k 6

Order: — | Running…

θᵢ' = arg(Σ_j∈N(i) e^{iθⱼ}) + ξᵢ

Topological (metric-free) flocking: Ballerini et al. 2008 showed starlings interact with fixed ~7 nearest neighbors regardless of distance. Voronoi tessellation defines neighbors. Order parameter φ = |Σe^{iθ}|/N.

Topological Flocking — Voronoi Neighborhoods