Fireflies

A meadow of Photinus carolinus, the synchronous fireflies of the Smoky Mountains. One firefly alone has no rhythm. Add more and watch a beat appear that nobody is keeping.

Start with one. It flashes, goes dark for a random while (seconds, sometimes minutes), and flashes again, with no rhythm at all. Then add more. Each firefly charges slowly toward a flash; seeing others flash gives it a small push. Past a certain crowd, flashes start arriving together in bursts, and the gap between bursts settles near the shortest rest any single firefly needs. Nobody leads. Whoever is ready first goes, and the rest are pulled along.

Based on Sarfati et al., "Emergent periodicity in the collective synchronous flashing of fireflies" (eLife, 2023), simplified. Each firefly charges toward a flash at its own random pace (rests of at least 5.7 s, usually tens of seconds, a stand-in for their lone-firefly data). After flashing it can't be hurried for 5.7 s; after that, every new flash it sees bumps its charge a little. The paper spreads the nudge over the whole crowd; I use a per-flash bump instead, because when I tested the paper's form at large crowds it stopped making bursts (their fits only go up to 20 fireflies). Measured over 30 simulated minutes: 3 fireflies, 26% of flashes in bursts; 40, 96%; 120, 100%, with bursts about 6 s apart, right next to the 5.7 s rest. With listening at zero, no bursts at all. Time runs about 8× fast.