On some riverbank trees in Southeast Asia, thousands of male fireflies switch on and off together, like one enormous lamp. Nobody is in charge. Each insect only watches the flashes around it.
Below is a meadow of simulated fireflies. Each one starts at a random point in its flash cycle. Watch the chart as they find each other: when the bars turn into tall, narrow spikes, the meadow is flashing as one.
The model behind the field is simple enough to fit in a paragraph. Each firefly has a number that climbs from 0 to 1 at a steady pace. When it reaches 1 the firefly flashes and its number drops back to 0. Alone, that makes a regular blink. In this field the natural pace differs a little from insect to insect, so no two clocks agree.
The only extra rule is a reaction. When a firefly sees a neighbour flash, it nudges its own number toward that flash: forward if it was nearly ready to flash, back a little if it had only just flashed. That is it: no leader, no shared clock, no messages other than light.
A nudge shortens the wait for a firefly that was almost ready. It can jump over the line and flash right away, in the same instant as the one it saw. One that had only just flashed is pushed back toward the flash instead. From then on those two flash together. Their combined light now nudges a third, then a fourth, and the group grows until it swallows most of the meadow.
In 1990 the mathematicians Rennie Mirollo and Steven Strogatz proved that a simple set of firefly-like oscillators, all connected, will almost always end up synchronised, however many there are. Try the sliders. At zero reaction nothing ever lines up. At a gentle reaction the field takes longer to line up. At a strong reaction it locks in within a few cycles.
Now drag the number of fireflies down to one. A lone firefly has nobody to react to, so there is nothing to line up with. The crowd is what makes the rhythm.
The real thing is messier than the model, and it is still being worked out. In Southeast Asia, males of species such as Pteroptyx malaccae and Pteroptyx tener gather on certain trees and flash in unison to attract females. A report of this from Thailand reached the West in the 1800s. In 1917 a letter in Science disputed it.
In the Great Smoky Mountains in Tennessee, Photinus carolinus does something different. In one field observation, each burst was up to eight quick flashes over about four seconds, then the forest went dark for roughly twelve seconds before the next burst. Bursts often start in one place and ripple through the trees at about half a metre per second, the same sort of wave you can start with a lantern tap above.
Researchers studying P. carolinus have reported that a lone firefly flashes at random intervals, sometimes seconds apart and sometimes minutes. In a group of fifteen or more in a tent, a shared beat appeared about every dozen seconds. That fits the idea that the rhythm belongs to the crowd and not to any one insect. Other species do it their own way: in South Carolina, Photuris frontalis has been recorded flashing mostly in rhythm while a few outliers keep their own period.
Pulse-coupled oscillators turn up far beyond insects. The 1990 proof built on earlier models of the heart's pacemaker cells, which also fire and reset together. A crowd's rhythmic applause can lock into step in a similar way: in a 2000 study in Nature, researchers recorded audiences after concerts and found the clapping alternating between random noise and a shared beat. Whenever many things tick, and each can hear the others, order can appear without anyone asking for it.
Set the reaction to the middle and press Scatter them three times. Does the meadow always find the same rhythm? Then tap a lantern right as a spike peaks and see how fast the crowd absorbs the nudge. Finally slow things down with the speed button and watch two fireflies merge, one jump at a time.