Density dependence of stripe formation in a cross-flow

Qualitative observations in ecological settings along with theoretical and numerical models suggest that when two different pedestrian streams cross a shared area, stripe-like self-organised structure emerge in order to minimise collisions and facilitate the flow. Although the phenomenon has been known for relatively long time, a systematic and quantitative verification of it through controlled experiment has been performed only recently. In this work we analysed such an experiment in which the geometry was kept fixed while changing density, in order to verify if there is a minimum density for stripe formation, and more in general the dependence on density of the phenomenon. An analysis based on two different observables, namely the angle identifying the position of the first neighbour in the same flow, and an order parameter to identify the direction of the environment presenting the higher regularity (the presence of a stripe) suggests that, although the stripe formation pattern is particularly strong at intermediate densities, the tendency to walk on a diagonal stripe is present also at considerably low densities.