The Firefly
Parliament.

Three hundred independent clocks. No conductor. No metronome. Under the right conditions, they begin to flash together.

LIVE SIMULATIONCLICK / TAP TO DISTURB

The night has no leader.00:00

Phase constellation

one dot per clock

When the dots gather, the arrow grows longer.

Coherence through time

0 = scattered · 1 = united

A collective rhythm can arise without any clock leading.

What am I watching?

Each light is an oscillator: it has a position in the garden, an angle on a clock, and its own preferred speed. The lights do not move toward each other. They adjust when they flash.

Every clock feels the average tug of the others. With weak influence, the fireflies drift apart. With sufficiently strong influence, a synchronized rhythm emerges, even though their preferred speeds differ.

Try Solitude, then Chorus. Once they synchronize, tap the night to disrupt a patch of clocks. Watch the collective rhythm recover—or fail to.

This is the Kuramoto model of coupled oscillators, presented as an imaginary firefly garden; it is not a literal model of firefly biology.

The small equation behind the spectacle

dθᵢ/dt = ωᵢ + (K/N) ∑ⱼ sin(θⱼ − θᵢ)

The angle θᵢ is one clock's phase, ωᵢ is its natural frequency, K is the strength of influence, and N is the population. The quantity displayed above the controls is

R = | (1/N) ∑ⱼ exp(iθⱼ) | .

When phases are scattered around the circle, they cancel and R is near zero. When all phases agree, R = 1.

“At first, each lantern insisted on its own time. Then the darkness discovered a pulse.”