Fireflies

A night meadow, and a few hundred fireflies flashing on their own clocks. You hold a lantern: hold to gather light, let go to flash it. A firefly that was nearly ready to flash answers yours at once; one that was not has its clock nudged toward you. Flash in the meadow's rhythm and it follows you; flash in your own and most of it ignores you. A meadow is done when it keeps one beat without you. Nothing is lost and nothing is timed.

How Clocks That Only Nudge Each Other Fall Into Step

Nothing in the meadow leads. Each firefly runs a clock, flashes when it comes round, and every flash it sees moves its own clock - forward if it was past halfway, back if it was not. That is the whole rule, and it is enough. Kuramoto showed in 1975 that oscillators coupled even weakly fall into step once the coupling outweighs the spread in their natural rates, and Mirollo and Strogatz showed in 1990 that clocks which only pulse at each other - which is what a flash is - get there from almost any start. Real fireflies do both halves of it: males of some Southeast Asian species hold a rhythm together in a mangrove for hours, and in the southern Appalachians one species flashes in bursts that roll through the trees. It is the same mathematics as a room of people clapping into time, and as the pacemaker cells that agree on a heartbeat.

How to play

• Hold the mouse, a finger or Space to gather light, and let go to flash. The longer the hold, the further the flash reaches.
• Let go at the moment the fireflies near the lantern flash. Off their beat, only the few that were about to go anyway answer.
• These fireflies follow a lantern flashed from about 15 percent faster than their own rhythm to about 10 percent slower, and ignore it outside that - it is easier to hurry a firefly than to hold one back.
• The ring in the corner fills as the meadow comes into step, counting every part of the meadow equally. Seven meadows, and a free one with no goal.

Read more: Emergence