Fireflies, and the
virtue of falling out of step
A field of fireflies, each blinking on its own clock. Turn up how much they watch each other and they synchronize, as Photinus carolinus does in the Southern Appalachians every June. Passing a signal around asks them to spread out again. Two needles point apart.
A Kuramoto explorable · a model written for fireflies · Brokenbranch Lab
Watch the field: each firefly blinks on its own clock. The slider sets how closely they watch one another. Near the middle, the field is most sensitive to a nudge. At the loose end, a single flash travels most cleanly because fewer neighbors flash over it. The two dials disagree.
Responsiveness
how alive to a nudge the whole field is — its sensitivity. The "edge of order" prize.
Coordination
how cleanly one firefly's flash gets through without others stepping on it. The signalling prize.
When one flash becomes a crowd
These dots are fireflies; the one knob sets how closely each watches its neighbors. Enough coupling makes the field flash together, like Southern Appalachian fireflies in June. Perfect unison is terrible for passing a message because every flash lands on top of every other. Clean signalling wants the field spread out and taking turns. An earlier version of this research treated responsiveness and coordination as one phenomenon. The toy pulled them apart.
From private clocks to one pulse
Each dot is a firefly with its own natural blink rhythm. The knob controls how much each one adjusts toward the others it can see; physicists call that coupling. At zero, they blink as a scatter of private clocks. Turn it up and they pull on one another until the whole field flashes as one. This is the Kuramoto model, one of the models written to explain fireflies.
Photinus carolinus lives in the Southern Appalachians, including the north-Georgia mountains and the Smokies. For a couple of weeks each late spring, the males flash together in bursts of five or six and then go dark together. Most fireflies keep their own time. The big-dipper firefly crossing a back yard answers no conductor.
So which is "better organized"? That's the trick of this toy. There are two different prizes, and they pull in opposite directions:
Responsiveness measures how ready the whole field is to swing after a nudge. It peaks at partial synchrony, near the edge where order forms. The amount of togetherness at that edge fades as the crowd grows, roughly as N−0.4. Our first 40% figure belonged to a field of 24 fireflies. It did not generalize. Daido (1990); Hong, Chaté, Tang & Park (2015).
Coordination asks whether one firefly’s flash gets through without its neighbors flashing over it. Synchrony piles the flashes into a wall of light. Clean signalling wants the fireflies spread out and taking turns.
We also expected a clever rhythm to beat plain randomness. It did not. Random spreading worked as well as every schedule we built; spacing mattered, choreography did not. The earlier headline joined responsiveness and coordination into one cross-scale phenomenon. This toy records the correction. The responsiveness peak comes from Daido (1990) and Hong, Chaté, Tang & Park (2015); the desynchronization result follows DESYNC (Degesys et al., 2007) over slotted ALOHA (Abramson, 1970). We put both measures on fireflies and watched the needles separate.
In early June the fireflies come out across Georgia, and that same week the synchronous display peaks up in the Blue Ridge. The ones in the yard, each blinking on its own clock, look like the disorganized ones. They aren't. They're organized for the other prize: every one of them gets a clean turn to be seen. Falling out of step is its own kind of keeping time.