Collective migrantion and pattern formation with zero-range interactions

We investigate the collective migration and pattern formation potential of zero-range-interacting agents, that is, agents interacting exclusively with others at exactly the same position. To this end, we use a lattice-gas cellular automaton model with no exclusion principles and polar/nematic velocity alignment interactions. We find that, in the case of polar alignment, the model shows a transition towards a highly ordered and condensed state with moving point clusters. In the nematic case, we observe the formation of high density, nematically-ordered bands. This suggests that migration is enough to relay information among individuals and to generate collective effects at the population level, even in the absence of spatially extended sensing.