Mathematical Modeling of Bird Murmurations

Self-motivated collective motions, which superficially seem to be in violation of the second law of thermodynamics by decreasing entropy, arise throughout physics, chemistry and biology. A well-known example in a petri dish is the spontaneous emergence of spiral waves in the so-called Belousov–Zhabotinski reaction. In biology, morphogenesis is another example in the differential development of bone and muscle in a growing organism. Collective motion is also found in various bird and animal systems where long-range information exchange is obtained by vision, and we here focus on the spectacular synchronized flying of flocks starlings in what are called murmurations. Recent work has shown how the birds can achieve this by focusing on dark-to-light edges in their distant view of the far-off flying birds. Averaging unit vectors that point at these edges defines, with other clues, their instantaneous flight instructions.