Human murmuration, Hierarchy, torus
As a term, swarming is applied particularly to insects, but can also be applied to any other entity or animal that exhibits swarm behaviour. The term flocking or murmuration can refer specifically to swarm behaviour in birds, herding to refer to swarm behaviour in tetrapods, and shoaling or schooling to refer to swarm behaviour in fish. Phytoplankton also gather in huge swarms called blooms, although these organisms are algae and are not self-propelled the way animals are. By extension, the term “swarm” is applied also to inanimate entities which exhibit parallel behaviours, as in a robot swarm, an earthquake swarm, or a swarm of stars.
From a more abstract point of view, swarm behaviour is the collective motion of a large number of self-propelled entities. From the perspective of the mathematical modeller, it is an emergent behaviour arising from simple rules that are followed by individuals and does not involve any central coordination. Swarm behaviour is also studied by active matter physicists as a phenomenon which is not in thermodynamic equilibrium, and as such requires the development of tools beyond those available from the statistical physics of systems in thermodynamic equilibrium. In this regard, swarming has been compared to the mathematics of superfluids, specifically in the context of starling flocks (murmuration).