Firefly Synchronization: Mirollo–Strogatz Pulse-Coupled Oscillators (2D)

This 2D companion trades the 3D forest scene for a plain canvas view built to make the underlying mechanism legible: each of N fireflies carries a phase that charges toward a flash threshold along a concave curve, and firing pulls every other firefly's charge forward by a tunable amount ε — the Mirollo–Strogatz pulse-coupled-oscillator model, the mathematically proven explanation for how real Pteroptyx firefly swarms lock into a single synchronized flash with no leader. A running Kuramoto order-parameter trace and a live phase-circle plot make the moment synchrony emerges — or fails to, at zero coupling — directly visible instead of implied.