Spontaneous emergence of milling (vortex state) in a Vicsek-like model

Collective motion is of interest to laymen and scientists in different fields. In groups of animals, many patterns of collective motion arise such as polarized schools and mills (i.e. circular motion). Collective motion can be generated in computational models of different degrees of complexity. In these models, moving individuals coordinate with others nearby. In the more complex models, individuals attract each other, aligning their headings, and avoiding collisions. Simpler models may include only one or two of these types of interactions. The collective pattern that interests us here is milling, which is observed in many animal species. It has been reproduced in the more complex models, but not in simpler models that are based only on alignment, such as the well-known Vicsek model. Our aim is to provide insight in the minimal conditions required for milling by making minimal modifications to the Vicsek model. Our results show that milling occurs when both the field of view and the maximal angular velocity are decreased. Remarkably, apart from milling, our minimal model also exhibits many of the other patterns of collective motion observed in animal groups.