Fish school at extreme scale

Fish schools are known to exhibit global collective patterns such as polarized schooling, milling, and turning. But how stable are these states to increasingly large number of fish? Here, we employed a self-propelled particle model of fish based on data-inferred behavioral rules and all-to-all flow interactions, with individual swimmers represented by their dipolar far-field flow signature. With the aid of high-performance parallel computing, we studied the emergent collective patterns in large schools of the order of 10⁴ individuals. We found that the structures which emerge globally at lower number of fish (10-100), like milling, schooling, or turning, breakdown with increasing school size. Instead, the school dynamically scatters and reassembles into local structures with rich dynamics and polarization properties. We analyzed the correlation of fluctuation in dynamically changing polarized and rotationally-ordered schools, characterizing their splitting and rejoining processes. Moreover, we related the energy spectrum of unsteady large schools with the size of coherent small schools. These findings pave the way towards creating a novel data-driven framework for describing extreme active matter with free boundaries.