Synchronize with chaos: the flashing lights of a swarm of fireflies embody in nature what mathematics predicted

Synchronize with chaos: the flashing lights of a swarm of fireflies embody in nature what mathematics predicted

Fireflies’ synchronized light shows have fascinated observers for ages. Credit: Raphaël Sarfati, CC BY-ND

Imagine an ancient forest in the fading light of a summer evening. As the last rays of the sun disappear below the horizon, a small flash catches your eye.

You turn around, hold your breath; it flashes again, hovering 2 feet above the leaf litter. From across the dark clearing, a fleeting response. Then another, and another, and within minutes twinkling fireflies spread through the quiet woods.

At first, they seem disorganized. But soon a few coordinated pairs appear, small tandems flashing at the same tempo twice a second. The pairs merge into triads, quintuplets, and suddenly the whole forest vibrates with a common, scintillating rhythm. The swarm has reached synchronization.

Firefly congregations are sprawling speed-dating events. The flashes convey a courtship dialogue between the advertising males and the selective females. Shaped by the interplay of competition and cooperation between thousands of interacting fireflies, collective light patterns emerge, twinkling analogs to the whispers of flocks of birds melting together. The mystifying phenomenon of the flash synchronization of certain fireflies has intrigued scientists for more than a century.

Synchrony is ubiquitous throughout the universe, from electron clouds to biological cycles and planetary orbits. But synchrony is a complex concept with many ramifications. It encompasses various shapes and forms, usually revealed by mathematics and later explored in nature.

Take the swarm of fireflies. Wait a little longer and among the illuminated chorus, something else appears: A few discordant flashers secede and continue out of time. They flash in unison but keep a resolute lag with their conformist peers. Could this be proof of a phenomenon predicted by mathematical equations but never seen before in nature?

Synchrony, with a twist

Twenty years ago, while delving into the equations that form the framework of synchrony, physicists Dorjsuren Battogtokh and Yoshiki Kuramoto noticed something peculiar. Under specific circumstances, their mathematical solutions would describe an ambivalent set, showing generalized synchrony interspersed with some erratic and floating constituents.

Their model was based on a set of abstract clocks, called oscillators, which tend to align with their neighbors. The non-uniform state was surprising, since the equations assumed that all oscillators were exactly the same and equally connected to each other.

Spontaneous breaking of the underlying symmetry is something that usually bothers physicists. We cherish the idea that some order in the fabric of a system should translate into similar order in its large-scale dynamics. If the oscillators are indistinguishable, they must either all synchronize or all remain chaotic and show no differentiated behaviors.

This piqued the curiosity of many, including mathematicians Daniel Abrams and Steven Strogatz, who named the phenomenon “chimera”. In Greek mythology, the Chimera was a hybrid monster made of incongruous animal parts – thus an apt name for a hodgepodge of mismatched oscillator clusters.

At first, chimeras were rare in mathematical models, requiring a very specific set of parameters to materialize. Over time, learning where to spot, theorists began to discover them in many variations of these patterns, calling them “breathable”, “twisted”, “multi-headed” and other strange epithets. Yet it remained a mystery whether these theoretical chimeras were also possible in the physical world – or just a mathematical myth.

Fireflies in Congaree National Park flash in unison. 1 credit

A decade later, a few ingenious experiments set up in physics labs yielded the elusive chimeras. They involved finely tuned interaction networks between sophisticated oscillators. While proving that engineering the coexistence of consistency and inconsistency was a tricky but possible undertaking, they left the deeper question unanswered: Could mathematical chimeras also exist in the natural world?

It turned out that it would take a tiny luminescent bug to light them up.

Chimera in the midst of the flashing chorus of fireflies

As a post-doc at the Peleg Lab at the University of Colorado, I work to decipher the inner workings of firefly swarms. Our approach is based on the foundations of an unknown niche of modern physics: the collective behavior of animals. Simply put, the overarching goal is to reveal and characterize large-scale, spontaneous and unsupervised patterns in animal group dynamics. We then study how these self-organized patterns emerge from individual interactions.

Our latest study is published in Scientists progress.

Advised by knowledgeable firefly experts, my colleagues and I traveled across the country to Congaree National Park in South Carolina to hunt Photuris frontalis, one of the few North American species known to synchronize. We set up our cameras in a small clearing among the loblolly pines. Shortly after the first flickers broke through the twilight, we observed a very rhythmic, precise synchrony, seemingly as clean as predicted by the equations.

It was an enchanting experience, but one that left me thinking. I was concerned that this display was too orderly to allow us to deduce anything from it. Physicists learn things by watching their natural fluctuations. Here, there seemed to be little variability to study.

The timing shows up in the data as sharp spikes in the graph of number of flashes over time. These peaks indicate that most lightning occurs at the same time. When it doesn’t, the trace looks jagged, like squiggles. In our storylines, I first saw nothing but the flawless comb-like pattern of flawless synchrony.

It turned out that the Chimera was hiding in plain sight, but I had to scour further through the data to encounter it. There, between the light chorus peaks, a few shorter peaks indicated smaller factions in sync with each other but not with the main group. I called them “characters”. With the synchronized refrain, these incongruous characters form the chimera.

As in ancient Greek theatre, the chorus sets the background while the characters create the action. The two groups are intertwined, walking through the same scene, as we revealed from the three-dimensional reconstruction of the swarm. Despite the splitting of their rhythm, their spatial dynamics appear indistinguishable. The characters don’t seem to come together or follow each other.

This unexpectedly intertwined self-organization raises even more questions. Do the characters in the swarm consciously decide to detach themselves, perhaps to signal their emancipation? Or do they find themselves spontaneously trapped out of step? Can mathematical knowledge shed light on the social dynamics at play in luminous beetles?

Unlike the abstract oscillators in mathematical equations, fireflies are cognitive beings. They take in complex sensory information and process it through a decision pipeline. They are also constantly on the move, forming and breaking visual bonds with their peers. Streamlined mathematical models do not yet capture these complexities.

In the quiet woods, synchronized flashes and their dissonant counterparts may have illuminated a treasure trove of new chimeras for mathematicians and physicists to hunt.

More information:
Raphaël Sarfati et al, Chimera states among synchronous fireflies, Scientists progress (2022). DOI: 10.1126/sciadv.add6690

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