Fig. 7: Flow illustration for jamming and roundabout motion.

a, b Local density ρ_loc (single stream) with vision angle ψ = π/2 and inflow a Γ = 0.5 and b Γ = 4. As inflow Γ increases, a rotation phase with an asymmetric density distribution develops, as seen in (b). c, d Local density with ψ = π and inflow c Γ = 0.4 and d Γ = 0.6. At Γ = 0.4, there is no jamming, as can be seen by the ‘uniform’ inflow and outflow density lines. However, when Γ ≥ 0.5, the system enters a jammed state, characterized by the depleted outflow lines and enhanced local density at the inflow. In all panels, agents enter at the left and exit at the right, and data is shown for a single agent stream. The local density is estimated as \({\rho }_{{{\rm{loc}}}}={N}_{\delta T}{\tau }_{r}/({\rho }_{0}\delta T{R}_{0}^{2})\), where \({N}_{\delta T}{\tau }_{r}/(\delta T{R}_{0}^{2})\) is the average local density in a region of area \({R}_{0}^{2}\), and N_δT is the total number of agents counted in time δT = 2500τ_r. The data is normalized by the local density at the inflow estimated as ρ₀ = 6Γτ_r/(2πR_intR₀).