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Fireflies twinkle against a backdrop of stars in Congaree National Park. (Credit: Nolan Bonnie)

In the middle of the old-growth forests of in South Carolina, fireflies put on an other-worldly display every May. Thousands of male insects belonging to the species Photuris frontalis flash together at the same time and follow the exact same pattern—a synchronous light show you can see only in few places in the United States.

Scientists and nature lovers have long been fascinated by how such simple insects can work together in perfect harmony.

Owen Martin hunts for fireflies in Congaree using a red light. (Credit: Owen Martin)

In a new study, engineers from �鶹��Ѱ�����Boulder have uncovered the mathematical rules fireflies follow to sync up their flashes.

The team’s findings could one day lead to new designs for robots that move in swarms and could help scientists better understand other examples of synchrony in biology—such as neurons firing at the same time in the brain, or cells syncing to the body’s internal clock, also known as circadian rhythm.

“It’s magical,” said Orit Peleg, associate professor in the Department of Computer Science and the BioFrontiers Institute at �鶹��Ѱ�����Boulder. “At certain times of night, fireflies have a single rhythm for the entire group, and they’re very punctual.”

Peleg will at the in Denver. The researchers ahead of peer review.

In the study, the researchers exposed individual male fireflies to a dim LED light—almost like an artificial version of a firefly.

If that light blinked faster than the males, the insects tended to speed up their flashing. If the light blinked slowly, the insects slowed down.

Think of it like an audience member in a crowded concert hall who is trying to join others clapping along to the beat.

“This research opens the door to discovering other examples of synchronization in nature that we haven’t seen yet,” said Owen Martin, the lead author of the research who earned his doctorate in computer science from �鶹��Ѱ�����Boulder in 2025. ��

Old patterns

The graduate student spent several summers at Congaree over the course of the experiment.

It’s a swampy area where cypress and tupelo trees hundreds of years old tower over the landscape. Martin remembers spending nights watching the twinkling light from fireflies reflect on the water of the park’s Cedar Creek.

Firefly flashes while resting on vegetation. (Credit: Nolan Bonnie)

“It makes me think of what that part of the Earth was like before people were there,” he said. “There is this strong sensation that everything is old.”

To study those ancient rhythms, Martin and Peleg set up a unique experiment: The team gently captured male fireflies one-by-one, then brought them into a tent that was completely shaded from all outside light.

Martin then sat in the pitch black and shined the LED at the males.

He explained that, under natural circumstances, fireflies tend to flash about once or twice every second. The group set its own LED to blink anywhere between once every second to once every 300 milliseconds.

The fireflies kept the beat.

In particular, the insects were most likely to change their own rhythm when the LED blinked almost at the same time as the fireflies, but just a hair off. If the LED blinked right before the firefly, the male often rushed its next flash to catch up to the light. If the LED blinked right after, the firefly waited a little longer to make its next flash.

If the LED was way off from the fireflies’ natural behavior, in contrast, they usually ignored it.

“For a whole season, I spent pretty much every night in the dark watching lights blink at a fixed frequency,” Martin said. “Then, occasionally, I’d get this magical experience where I’d see the firefly just start syncing with the light. I would wonder if I was just seeing things.”

Swarming robots

He wasn’t. Drawing on their observations, Martin and Peleg developed what mathematicians call a “phase-response curve” for the firefly flashes—essentially, a formula that describes how an outside light source drives fireflies to change their own flashing patterns.

The researchers noted that the team still has a lot of work to do to understand Congaree’s magical fireflies.

For a start, males in the wild rarely just see a single other source of light as they did in the team’s experiments. Instead, they’re usually in groups of dozens or more fireflies, all blinking at the same time.

Engineers can also learn a lot from what fireflies do in the wild. Study co-author Kaushik Jayaram, an engineer at Imperial College London, noted that future drones could communicate using visual signals, similar to fireflies.

“Peer-peer optical communication can be lower power and more secure, resulting more efficient swarming and robust aggregations despite requiring line-of-sight, adding a complementary capability to today’s miniature SWAP-constrained drones which largely rely on radio frequency-based approaches,” Jayaram said.

Peleg added that she envisions a future in which fleets of tiny robots work together to complete tasks without any central command.

“If you’re trying to get a lot of robots to push a large object, and they’re pushing at different times, then they’re going to struggle,” she said. “But if they’re all pushing at the same time, they’ll be a lot more successful.”