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Swarmalators are oscillators that can swarm as well as sync via a dynamicbalance between their spatial proximity and phase similarity. We present ageneralized D-dimensional swarmalator model, which is more realistic andversatile, that captures the self-organizing behaviors of a plethora ofreal-world collectives. This allows for modeling complicated processes such asflocking, schooling of fish, cell sorting during embryonic development,residential segregation, and opinion dynamics in social groups. We demonstrateits versatility by capturing the manoeuvers of the school of fish and travelingwaves of gene expression, both qualitatively and quantitatively, embryonic cellsorting, microrobot collectives, and various life stages of slime mold by asuitable extension of the original model to incorporate appropriate featuresbesides a gallery of its intrinsic self-organizations for various interactions.We expect this high-dimensional model to be potentially useful in describingswarming systems in a wide range of disciplines including physics of activematter, developmental biology, sociology, and engineering.

Exotic swarming dynamics of high-dimensional swarmalators