Flocks and Schools as Living Lattices
New York University mathematicians have discovered that the synchronized movements of bird flocks and fish schools mirror the behavior of soft crystalline materials. According to a study published in Physical Review Fluids, individual animals function like atoms in a lattice, held in repeating, orderly patterns by flexible, spring-like bonds.
The Mechanics of Collective Stability
Led by Leif Ristroph, director of NYU’s Applied Mathematics Laboratory, the team developed a model to explain how these groups maintain their structure. The study posits that collectives function as “soft crystals”—ordered solids capable of rapidly altering their properties in response to external stimuli like temperature, physical force, or environmental flows.
“Lines of birds or fish behave like an elastic material with regularly spaced individuals held together by flexible, or spring-like, bonds,” said Christiana Mavroyiakoumou, a former researcher at NYU’s Courant Institute who contributed to the study.
By treating animals as “atoms,” researchers identified why these formations remain stable yet adaptable. This inherent “fragility” is a functional advantage, allowing the group to sense and respond immediately to predators, obstacles, or shifts in air and water currents.
Validation Through Mechanical Flapping
To verify the model, the team used 3D-printed, mechanized flappers designed to mimic bird wings. Operated in water, these devices simulated the aerodynamics of flight and the way air interacts with wing structures.
The experiments confirmed the mathematical predictions: when moving as a group, the flappers spontaneously organized into queues or columnar formations. This “mock flock” maintained spacing and cohesion exactly as soft crystalline substances do.
Engineering Applications for Autonomous Swarms
These findings offer new frameworks for understanding biological coordination, with direct implications for human-engineered systems. The principles governing how birds and fish manage aerodynamic and hydrodynamic interactions are highly relevant to several fields:
“Because these movements are similar to those that form the building blocks of materials, the work opens new avenues for analyzing—and potentially manipulating—how these components interact,” Ristroph noted.
The research, supported by a grant from the National Science Foundation, clarifies the physical rules that allow biological groups to remain both organized and responsive to their surroundings.