Supplementary material from "Lévy walk process in self-organization of pedestrian crowds"

Similar to other animal groups, human crowds exhibit various collective patterns that emerge from self-organization. Recent studies have emphasized that individuals anticipate their neighbours' motions to seek their paths in dynamical pedestrian flow. This path-seeking behaviour results in deviation of pedestrians from their desired directions (i.e. the direct path to their destination). However, the strategies that individual adopt for the behaviour and how the deviation of individual movements impact the emergent organization are poorly understood. We here show that the path-seeking behaviour is performed through a scale-free movement strategy called a Lévy walk, which might facilitate transition to the group-level behaviour. In an experiment of lane formation, a striking example of self-organized patterning in human crowds, we observed how flows of oppositely moving pedestrians spontaneously separate into several unidirectional lanes. We found that before (but not after) lane formation, pedestrians deviate from the desired direction by Lévy walk process, which is considered optimal when searching unpredictably distributed resources. Pedestrians balance a trade-off between seeking their direct paths and reaching their goals as quickly as possible; they may achieve their optimal paths through Lévy walk process, facilitating the emergent lane formation.