Flocking — Topological (Voronoi) Neighbors

Empirical studies of starling murmurations (Ballerini et al. 2008) found birds interact with their 6–7 nearest topological neighbors, not all within a fixed radius. Explore how this changes flocking.

Flock

Interaction Rule

Order Φ0.00
Mean heading
Rule
Topological vs. Metric
Metric: interact with all birds within radius R. Robust to density but not to density fluctuations.

Topological: interact with k nearest neighbors regardless of distance. STARFLAG project (Rome 2008) showed starlings use k≈7. This makes the flock robust to density perturbations — a predator can't isolate birds by just stretching the flock.