Each firefly has its own natural rate ω and a phase θ that runs once around the 720° dial (two turns: the outer ring, then the inner). Each one nudges toward the crowd by K·r·sin(ψ − θ), and it flashes as it passes 0°.
Tap to raise the coupling K. The gold hand is the crowd’s mean phase, and its length is r. The same ?seed= always gives the same run.
LITThe Kuramoto model (1975), in mean-field form. Every phase must stay inside [0°, 720°) and r inside [0, 1], or the page throws.
AMBERThe 720° dial is the site’s spinor clock. Kuramoto itself is 360°; here the phase is drawn at half-angle.