Fig. 5: Phase transitions in collectives with an egocentric representation of space.

A, B The distributions of global order (GO) and local order (LO) in groups of various sizes of agents with egocentric representation of space for different values of total social attraction, \({h}_{{{{\rm{t}}}}}^{{{{\rm{s}}}}}\), are plotted. By increasing \({h}_{{{{\rm{t}}}}}^{{{{\rm{s}}}}}\), the system shows a phase transition from a disordered phase, where individuals move independently, to an aggregation phase, where individuals form aggregates, and no collective motion is observed. While GO takes a small value and does not show sensitivity to social attraction (indicating no collective motion exists), LO shows bimodality close to the order-disorder transition, indicating a discontinuous transition from the disordered phase with low LO to the aggregation phase with high LO. C, D Snapshots of the collective behavior in the ordered phase are shown. For large β (low network noise), in the ordered phase, agents form an almost stationary circular pack of densely aggregated agents. For smaller β, the pack’s radius increases, and agents perform a random walk-like movement within the pack. C shows a snapshot of a dense pack for large β and D shows trajectories of the individuals within a pack for smaller values of β. Local order is high in both cases. Parameter values: N_s = 100, v₀ = 10, σ = 2π/N_s, h_b = 0, β = 400, N = 80, and L = 1000.