Fig. 4: Path-length probability distribution.

Probability distribution P of the path length l_p for a different relative maneuverability (ψ = π/2, Pe = 100) and (b) different vision angles (Δ = 8, Pe = 100). For small Δ, the paths are nearly straight and the probability distribution is well approximated by Eq. (9) (dashed line). In scenarios characterized by high maneuverability (Δ) and large vision angles (ψ), agents traverse longer paths within the interaction sphere to navigate around others. This behavior yields a log-normal distribution for the path length, with the black solid line representing a fitted log-normal model to the data. The path lengths are only determined for trajectories that successfully reach the exit (see “Methods”) and are averaged over different agent types. The data is collected for times 4t₀ < t < 16t₀ and averaged over all agents, where t₀ = 2R_int/v₀.