Fireflies in a South Carolina swamp revealed the math behind synchronized flashing

Every May, in the old-growth forests of Congaree National Park in South Carolina, thousands of male Photuris frontalis fireflies flash in unison. The synchronous light show - one of only a few visible in the United States - reflects off the dark water of Cedar Creek and has drawn scientists and visitors for years. But the mathematical rules governing how individual insects, each operating with a tiny nervous system, achieve collective precision have remained elusive.

Owen Martin spent several summers finding out. The CU Boulder doctoral student sat alone in a lightproof tent in the swamp, in complete darkness, shining a small LED at individual captured fireflies and recording what happened.

One firefly, one LED, total darkness

The experimental setup was deliberately minimal. Martin and his advisor, Orit Peleg, associate professor of computer science at CU Boulder, wanted to isolate the response of a single firefly to a single light source - removing the complexity of a group. Under natural conditions, fireflies flash roughly once or twice per second. The researchers set their LED to blink at rates ranging from once per second to once every 300 milliseconds.

The fireflies adjusted. When the LED blinked slightly before the firefly's natural flash, the insect rushed its next flash to catch up. When the LED blinked just after, the firefly waited a bit longer. The key was proximity: the LED had to be close to the firefly's own rhythm to trigger adjustment. If the LED timing was far off, the insect ignored it entirely.

Think of someone trying to clap along at a concert. If the crowd's rhythm is close to yours, you adjust. If it is wildly different, you give up.

Building the phase-response curve

From hundreds of these one-on-one interactions, Martin and Peleg constructed what mathematicians call a phase-response curve - a formula describing exactly how an external light source drives a firefly to adjust its own flashing pattern. This curve is the fundamental building block for modeling how synchronization emerges in large groups. If you know how one individual responds to one neighbor, you can, in principle, simulate how thousands coordinate.

The researchers presented their findings at the American Physical Society's 2026 Global Physics Summit in Denver on March 16. The results were published online ahead of peer review.

Why synchrony matters beyond fireflies

Synchronized flashing is one instance of a broader phenomenon that appears throughout biology. Neurons fire in synchrony to encode information. Heart pacemaker cells synchronize to maintain rhythm. Circadian clock cells coordinate to keep the body on a 24-hour cycle. In each case, individual oscillators with slightly different natural frequencies manage to lock together.

The mathematical principles governing these systems share deep structural similarities. Understanding how fireflies do it - organisms simple enough to study in controlled isolation but complex enough to exhibit genuine collective behavior - provides a tractable entry point into a problem that spans neuroscience, cardiology, and chronobiology.

From swamps to swarm robotics

The findings also have engineering applications. Study co-author Kaushik Jayaram, an engineer at Imperial College London, noted that peer-to-peer optical communication - where robots use light signals to coordinate, much like fireflies - could be lower power and more secure than current radio-frequency approaches for drone swarms. Line-of-sight is required, which limits range, but for applications where miniature robots need to coordinate in close proximity, the firefly model is attractive.

Peleg envisions fleets of tiny robots pushing a large object in unison, using synchronized timing to coordinate force. Push at different times, and the robots struggle. Push together, and they succeed. The phase-response curve provides the mathematical foundation for that coordination.

What remains unknown

The study examined individual fireflies responding to a single LED. In the wild, each insect is surrounded by dozens or hundreds of flashing neighbors. How the one-to-one response rules scale to large groups is a separate problem - one that likely involves nonlinear dynamics, spatial effects, and signal interference that the current experiment was not designed to capture.

The results have not yet undergone formal peer review, though they were presented at a major physics conference. And the species studied, Photuris frontalis, is just one of roughly 2,000 firefly species worldwide. Whether other synchronizing species use similar mathematical rules or have evolved different solutions remains an open question.

Martin recalls the moment it all clicked during one of his solo sessions in the dark: the firefly began syncing with his LED, its flash locking into rhythm with the artificial light. He wondered briefly if he was imagining it. He was not.