Sync order r = 0.00
Mean phase drift = 0.00 rad/s
Flashes/s = 0

Each firefly is a phase oscillator θᵢ obeying the Kuramoto coupling law dθᵢ/dt = ωᵢ + (K/N)Σⱼ sin(θⱼ−θᵢ), with its own natural frequency ωᵢ drawn from a normal distribution of width σ. A firefly flashes when its phase crosses 2π. Raise K and synchrony (order parameter r = |⟨e^{iθ}⟩|) emerges from the crowd; raise σ and the frequency spread fights it back into disorder — the same competition that synchronizes real Photinus carolinus swarms. Drag to orbit the forest, scroll to zoom.