Fig. 6: Collective behavior in small groups of agents with an allocentric representation of space.

A, B The distribution of GO and LO in groups of various sizes of agents with allocentric representation of space close to the order-disorder transition (A) and close to the collective motion-aggregation phase transition (B). In both cases, the distribution shows bimodality, signaling a discontinuous pseudo-phase transition in small system sizes. C, D GO and mean distance between all pairs normalized by space size, L, as a function of time for different values of total social attraction are plotted. For small social attraction, the system shows intermittency between high and low order, and for larger social attraction, intermittency between ordered motion and aggregation is observed. E–G Example snapshots of motion patterns from the Supplementary Videos for some values of \({h}_{{{{\rm{t}}}}}^{{{{\rm{s}}}}}\) shown in (A, B). In the collective motion phase, the system shows a rich set of motion patterns, including swirling in circular orbits (E), or in coil-shaped orbits (F), fission-fusion dynamics, and intermittency between highly ordered motion and aggregation (G). Parameter values: N_s = 100, v₀ = 10, σ = 2π/N_s, h_b = 0, β = 400, N = 10, and L = 1000.