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Murmuration: What Engineers Can Learn from Flocking Birds

Written by El Hebert '24

Edited by Wonjin Ko '26

In Hannover, Germany, starlings fly together as one cohesive flock. Bärbel Miemietz, 2022, hosted on Wikimedia Commons.

Geese line up in V formation, pigeons lift off as one to avoid a passing car, and the starling colonies of Europe form shifting swarms of thousands of individuals, known as murmurations. It’s an everyday phenomenon, as beautiful as it is mysterious: “birds of a feather flock together” for defense and efficient flight, coordinating rapid synchronized motion without any leaders or planning. How do they do it?

“Animals are amazing machines,” says Professor Kenneth Breuer, a researcher here at Brown. He’s one of many scientists around the world dedicated to the study of birds in motion. By releasing starlings into a wind tunnel in his lab, he can measure their movements and responses to disturbances in the air, such as a rising thermal or the wake of a fellow bird. But he’s not a biologist – in fact he’s the Director of the Center for Fluid Mechanics at Brown. As it turns out, the techniques of engineering, when applied to flying birds, can help reveal the patterns and instinctive strategies behind their movements.

The sight of a coordinated flock in action has long dazzled casual observers and scientists alike. In 1932, ornithologist Edmund Selous speculated that such behavior could only be explained by telepathic “thought-transference” [1]. Four decades later, W.D. Hamilton, a British evolutionary biologist, first proposed a simple model for the evolution of dense herd behavior: the Selfish Herd Hypothesis states that in a dangerous situation, flocks or herds form as each individual takes cover behind its neighbors. In other words, safety in numbers [2].

Flocking together also lets birds take advantage of each other’s aerodynamics, riding the wakes of their fellow fliers. Hence the V formation of migrating geese.

Starlings don’t form the same steady assemblies as the long-distance flying geese, but Professor Breuer’s work has shown that they move toward their neighbors to save energy. “The birds like to position themselves in specific locations behind each other,” he says. “We’ve found that they do tend to save energy when they fly in these formations.”

His lab can physically track a bird’s energy use through a procedure called NABI, which involves a harmless injection of sodium bicarbonate laced with a heavy form of carbon. As the bird works to fly against the streaming currents of the wind tunnel – “a treadmill for birds” – its metabolism converts the heavy bicarbonate to heavy carbon dioxide, which is exhaled, then detected and measured. Just like humans, birds metabolize faster when they’re putting in an effort.

Energy and safety may explain why animals like birds flock, but not how. And the problem of how can be a thorny one. For each individual, the rules of movement must be simple and robust (after all, starlings and fish aren’t doing complex topology in their heads) — but thorough enough to create the dynamic patterns we see. Luckily, computer simulations now allow scientists to test proposed rules on artificial flocks, modeling animals as moving particles that can respond to one another. For example, in 2002, Steven Viscido, Matthew Miller and David S. Whetley used this technique to show that the best flocking rules account for both the general “crowdedness” of the animal’s field of view, and the specific movements of its near neighbors [3].

Also thanks to new advances in technology, researchers can now map real, living murmurations in all their glory. In Rome, the STARFLAG project uses a multiple-camera network to capture 3-D video of starling flocks in action, each one several thousand birds strong. STARFLAG revealed new mathematical details in the starlings’ response to motion and closeness, suggesting that birds don’t prioritize their neighbors’ influence based on distance, but rather try to maintain contact with a certain number of birds, no matter how widely spread. For the starlings of Rome, this magic number is 6 to 7 [4, 5].

“There we’re pretty sure it’s a visual connection,” says Professor Breuer. “In our case there’s certainly a visual component, but I think there’s also a sensory component… They feel it’s a little easier to fly in a certain location. Once you get into position, you feel a bit of that lift.” In the Breuer lab, the lift can be visualized with a puff of fine particles that blow in the wind tunnel, showing air disturbances created and responded to by the starlings. This technique, known as particle image velocimetry, is a standard in fluid dynamics.

Flock research often cuts across field lines, involving biology, engineering, math, and computer science. Professor Breuer himself came from a pure engineering background, and began collaborating with the Biology department when he first came to Brown in 1999. Professor Sharon Swartz, a bat biologist, introduced him to the field of animal locomotion. She still works on a captive colony of bats here, and the two have now collaborated for 23 years.

Professor Breuer describes how his work has given him a new appreciation for biology, and the way it intersects with engineering. His subjects “can move efficiently and with great control through a fluid,” he says. “How did these animals get to be the way they are? What are the pressures that drove their evolution? How do the various muscles and sensory systems work together to achieve that? It’s a beautiful thing to ask.”

If nature is the greatest engineer, then can we humans draw inspiration from it for our own inorganic technology? Absolutely, according to the world of bio-informed design. “Taking ideas from biology is a great way to do engineering,” says Professor Breuer. He and many other flock researchers hope to see efficient flying behavior implemented in aerial robots. Flapping flight is much more maneuverable, and much less noisy, than the current quadcopter drones used for everything from search and rescue to filmmaking. Furthermore, coordinated swarming could inform self-driving cars [6], collaborative transport machines, and even fast automatic radiation measurements [7].

Recently, some social scientists have proposed that human behavior on social media can be modeled as a murmuration too: clusters of like-minded individuals that all take cues from each other when forming opinions [8]. If you feel that you or someone you know may be part of a murmuration, you might want to give Professor Breuer a call. After all, he’s looking for undergraduate researchers for the summer.



[1] Selous E. Thought-Transference-or What?-in Birds. Constable & Company; 1931. Cited 6 Mar 2023.

[2] Hamilton WD. Geometry for the selfish herd. Journal of theoretical Biology. 1 May 1971 [cited 6 Mar 2023];31(2):295-311. DOI: 10.1016/0022-5193(71)90189-5.

[3] Viscido SV, Miller M, Wethey DS. The dilemma of the selfish herd: the search for a realistic movement rule. Journal of theoretical biology. 21 Jul 2002 [cited 6 Mar 2023];217(2):183-94. DOI: 10.1006/jtbi.2002.3025.

[4] King AJ, Sumpter DJ. Murmurations. Current Biology. 21 Feb 2012 [cited 6 Mar 2023];22(4):R112-4. DOI: 10.1016/j.cub.2011.11.033.

[5] Ballerini M, Cabibbo N, Candelier R, Cavagna A, Cisbani E, Giardina I, Lecomte V, Orlandi A, Parisi G, Procaccini A, Viale M. Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proceedings of the national academy of sciences. 29 Jan 2008 [cited 6 Mar 2023];105(4):1232-7. DOI: pnas.0711437105.

[6] Sánchez NC, González JM, Pastor LA, Larson K. Future urban mobility as a bio-inspired collaborative system of multi-functional autonomous vehicles. arXiv preprint arXiv:2106.09543. 15 Jun 2021 [cited 6 Mar 2023]. DOI: 10.48550/arXiv.2106.09543.

[7] Petráček P, Walter V, Báča T, Saska M. Bio-inspired compact swarms of unmanned aerial vehicles without communication and external localization. Bioinspiration & Biomimetics. 18 Dec 2020 [cited 6 Mar 2023];16(2):026009. DOI: 10.1088/1748-3190/abc6b3.

[8] Zhang Y, Chen F, Rohe K. Social media public opinion as flocks in a murmuration: Conceptualizing and measuring opinion expression on social media. Journal of Computer-Mediated Communication. 21 Dec 2022 [cited 6 Mar 2023];27(1):zmab021. DOI: 10.1093/jcmc/zmab021.

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