Fireflies in step
Ten thousand clocks, each pulled a little toward all the others: past one coupling strength they fall into step, and no clock leads.
No leader. Past one coupling strength, ten thousand clocks agree.
Every dot is a clock with its own natural rate, coloured by its phase, and it flashes once per cycle. Each one is pulled toward the average of all the others with a strength K: the Kuramoto model, 1975. Some fireflies flash in unison the same way, whole trees at once, with nothing conducting them (Buck & Buck, 1968).
Through the loop K rises. Below a critical value the clocks ignore each other and the field is confetti. Past it, a group locks and grows. The gauge is r, how much they agree, from 0 to 1. The dashed curve under it is the theory for infinitely many clocks: the measured line lags it while K climbs, then sits on it.
At the end, 9,293 of the 10,000 are in step. The rest run too fast or too slow to be caught.
The reel carries sound made by the same clocks, a click each time one completes a cycle: hiss while they disagree, a kick drum once they agree. The loop here is silent.
Rendered offline in Canvas2D by a seeded module, seed 7. No camera, and nothing leaves the machine.