Flocking birds and schools of fish are a familiar sight. While previous research has uncovered the broad dynamics driving these movements, their underlying intricacies remain a mystery. Now a study by a team of New York University mathematicians offers new insights into these phenomena. It reveals that flocks and schools behave in ways similar to a soft crystalline material, with individual birds and fish serving as “atoms” that are evenly spaced in a lattice-like formation.

The findings, reported in the journal Physical Review Fluids, offer detailed insights into the hydrodynamic and aerodynamic interactions crucial in aerospace and automotive engineering, robotics and energy harvesting.

“Our findings offer a new way to understand how animal collectives coordinate movement and respond to their environment,” says Christiana Mavroyiakoumou, a researcher at NYU’s Courant Institute School of Mathematics, Computing, and Data Science at the time of the study and now a fellow at Oxford University’s Mathematical Institute. “More specifically, lines of birds or fish behave like an elastic material with regularly spaced individuals held together by flexible, or spring-like, bonds—akin to soft crystalline substances in which atoms are arranged in an orderly, repeating pattern.”