Fireflies adjust their flash timing when they see neighbors — global sync emerges from local rules
Firefly Field
Order Parameter (synchrony)
Order parameter R = 0.00
Mirollo-Strogatz model: each firefly has phase θ ∈ [0,1]. When θ=1 → flash and reset to 0.
On seeing a neighbor flash within range: advance own phase by ε (clamped to 1).
All-to-all coupling at high ε → rapid synchronization. Local coupling → slower, wave-like sync.
Order parameter R = |⟨e^{2πiθ}⟩| measures how clustered the phases are. R=1 → perfect sync.