In the 1990s, a Tennessee naturalist named Lynn Faust read a scientist's statement that there were no synchronous fireflies in the US. Faust knew what she was seeing when she was in the woods.

The species of Photinus carolinus is found in the Great Smoky Mountains. There are clouds of male fireflies in the sky. The fireflies emit a burst of quick flashes within a few seconds, then go quiet for several times before losing another burst. Imagine a crowd of people waiting for celebrities to show up, snapping photos at each appearance, and then twiddling their thumbs in the downtime.

The isolated firefly tried to flash on beat with a neighboring firefly in a nearby jar. High-sensitivity video cameras were set up at the edges of fields and forest clearings. The footage was counted by the number of fireflies illuminated at a time. Statistical analysis of this painstakingly gathered data proved that all the fireflies within the cameras view at a scene really did emit flash bursts.

Better technology was available when Peleg and her colleague, the physicist Raphal sarfati, set out to collect firefly data. A system of two cameras was designed. The dynamics of firefly swarms can be captured from within, not just from the side. Instead of counting flashes by hand, Sarfati came up with a way to triangulate firefly flashes caught by both cameras and then record where they happened.

The system was brought into the field in Tennessee in the summer of 2019. He had never seen a spectacle with his own eyes. The Tennessee bursts were messier, with bursts of up to eight quick flashes over about four seconds repeated roughly every 12 seconds. He felt that a system with wild fluctuations could be more informative than one that behaved perfectly. He said it was complex but also beautiful.

Random but sympathetic flashers.

She learned to understand them through a model created by the Japanese physicist and theoretical Biologist Art Winfree. The granddaddy of mathematical schemes that explain how synchrony can arise is the ur-model of synchrony.

Models of synchronous systems have to describe two processes. A lone firefly in a jar is governed by a behavioral rule that determines when it flashes. The flash of a firefly influences its neighbors. A lot of different agents can pull itself into a neat chorus.

The most famous model of synchronization was created by a professor of physics at Kyoto University.

Photograph: Tomoaki Sukezane

Each firefly is described in a way that makes it sound like it has a preferred rhythm. Imagine a bug flashing every time its pendulum sweeps through the bottom of it's arcs, as if it were a hidden pendulum. A firefly's pace-setting pendulum might be pulled forward or back by a neighboring flash. A collective governed by these rules will often converge on a coordinated flash pattern even if the fireflies start off out of sync.

Over the years there have been several variations on this general scheme. Strogatz and Rennie Mirollo of Boston College showed in 1990 that a very simple set of firefly-like oscillators would almost always work if you connected them. In the next year, Ermentrout explained how groups of Pteroptyx malaccae fireflies in Southeast Asia could sync up. A group led by Gonzalo Ramrez-vila of the Higher University of San Andrés in Bolivia came up with a scheme in which fireflies could switch between acharging and discharging state.