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When two streams of pedestrians cross at an angle, striped patternsspontaneously emerge as a result of local pedestrian interactions. This clearcase of self-organized pattern formation remains to be elucidated. Incounterflows, with a crossing angle of 180{\deg}, alternating lanes of trafficare commonly observed moving in opposite directions, whereas in crossing flowsat an angle of 90{\deg} diagonal stripes have been reported. Naka (1977)hypothesized that stripe orientation is perpendicular to the bisector of thecrossing angle. However, studies of crossing flows at acute and obtuse anglesremain underdeveloped. We tested the bisector hypothesis in experiments onsmall groups (18-19 participants each) crossing at seven angles (30{\deg}intervals), and analyzed the geometric properties of stripes. We present twonovel computational methods for analyzing striped patterns in pedestrian data:(i) an edge-cutting algorithm, which detects the dynamic formation of stripesand allows us to measure local properties of individual stripes; and (ii) apattern-matching technique, based on the Gabor function, which allows us toestimate global properties (orientation and wavelength) of the striped patternat a time T. We find an invariant property: stripes in the two groups areparallel and perpendicular to the bisector at all crossing angles. In contrast,other properties depend on the crossing angle: stripe spacing (wavelength),stripe size (number of pedestrians per stripe), and crossing time all decreaseas the crossing angle increases from 30{\deg} to 180{\deg}, whereas the numberof stripes increases with crossing angle. We also observe that the width ofindividual stripes is dynamically squeezed as the two groups cross each other.The findings thus support the bisector hypothesis at a wide range of crossingangles, although the theoretical reasons for this invariant remain unclear.

Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of `stripe' formation in human data