Researchers at New York University have uncovered a striking similarity between the coordinated movements of flocks of birds and schools of fish and the behavior of a soft crystalline material. The study, published in Physical Review Fluids, suggests that individual animals in these groups act like “atoms” in a lattice-like formation, evenly spaced and held together by flexible, spring-like bonds. This insight could reshape understanding of collective motion in biology and inspire applications in engineering and robotics.
Soft Crystalline Analogies
The research team, led by Christiana Mavroyiakoumou of NYU’s Courant Institute and Leif Ristroph, director of NYU’s Applied Mathematics Laboratory, found that these groups behave like soft crystals—materials that can change properties in response to external forces. In such materials, atoms are arranged in an orderly, repeating pattern, much like how birds or fish maintain regular spacing while adjusting to environmental changes.
“These movements resemble those of soft crystalline substances,” Mavroyiakoumou said. “Individuals in a flock or school are held together by flexible bonds, allowing them to shift positions quickly while maintaining overall cohesion.” The comparison highlights how both biological systems and materials can balance stability with adaptability.
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The study builds on earlier work by the same team, which explored how these groups avoid collisions and handle complex flows. This new research explores the precise mechanisms that allow such large-scale coordination. By modeling the interactions as those of soft crystals, the team identified a potential link between the fragility of these materials and the responsiveness of animal groups.
“Crystalline structures are inherently fragile because their positions are susceptible to deformations,” Mavroyiakoumou explained. “Similarly, birds and fish must constantly sense and react to external forces—like air currents or predator movements—to sustain their formations.” This fragility, paradoxically, may be an advantage, enabling rapid adjustments to changing conditions.
Experiments and Models
To test their hypothesis, the researchers conducted experiments using 3D-printed, motor-driven “flappers” designed to mimic the wing movements of birds. These devices, which flapped in water, replicated the columnar formations seen in flocks, where individuals line up directly behind one another. By varying the speed and configuration of the flappers, the team observed how the group self-organized into stable yet flexible patterns.
The results aligned closely with their mathematical model. The flappers, acting as proxies for birds or fish, adjusted their spacing and alignment in response to simulated environmental forces, much like the proposed soft crystalline analogy. This consistency suggests that the model captures key aspects of real-world collective motion.
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The study’s authors emphasized that their findings could have practical implications. For instance, understanding how these groups manage stability and adaptability might inform the design of drones or robotic systems that need to operate in dynamic environments. “The principles here could be applied to anything from swarm robotics to fluid trends in engineering,” Ristroph noted.
While the research offers a novel framework for analyzing collective motion, it also raises questions about how these systems might be influenced or controlled. Could similar principles be used to guide the movement of autonomous vehicles or improve energy-harvesting technologies? The team’s model provides a starting point, but further experiments and interdisciplinary collaboration will be needed to explore these possibilities.
The work was supported by a grant from the National Science Foundation, highlighting its potential to bridge fundamental scientific questions with real-world applications. As the researchers continue to refine their model, the analogy between soft crystals and animal collectives may open new avenues for both biological and engineering research.