Fireflies

A hundred and fifty fireflies sit in a dark field. Each one flashes on its own rhythm, a little faster or slower than the rest. Each one also watches the fireflies near it, and when a neighbor flashes a moment earlier, it nudges its own timing to catch up.

Things to try

Slide “how closely they watch each other” up and give it ten seconds. Small patches start flashing together, then grow, merge and roll across the field as waves.

Now make their rhythms more varied. The patches fall apart, and the fireflies need a closer watch on each other before they find the beat again.

Tap a firefly to knock it half a cycle out of step. Watch its neighbors pull it back.

A tipping point

Below a certain closeness, nothing happens: each firefly drifts at its own pace and the field flickers. Past it, sync appears and spreads. Yoshiki Kuramoto found this threshold in 1975 for oscillators that all see each other, and showed that it rises with how different their natural rhythms are. Here each firefly sees only its neighbors, so sync starts in patches and spreads from there.

Real fireflies do this. Photinus carolinus fills valleys in the Great Smoky Mountains with flashes in step every June, and Pteroptyx fireflies light up whole mangrove trees in Southeast Asia together.

The field keeps the flashing slow and soft so it stays comfortable to watch. Each firefly’s own rhythm stays under one flash a second, and a neighbor’s pull never pushes one past three a second, the accessibility limit for flashing content. If your device asks for reduced motion, the field starts paused, with a button to step forward.

Credits

Yoshiki Kuramoto, “Self-entrainment of a population of coupled non-linear oscillators” (1975). Steven Strogatz, “From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators” (Physica D, 2000), and his book Sync (2003), which tells the firefly story far better than this page can.