Walks of identical total length of 1,000 unit steps are shown drawn to scale. Lévy flights (or walks) have ultra-long steps, which are absent from Brownian walks. b, A close-up of the Brownian walk, in which the walker returns many times to previously visited locations (a phenomenon known as 'oversampling'). By contrast, the Lévy walker occasionally takes long jumps to new territory. This reduction in oversampling is part of the theoretical basis for interest in the Lévy-flight foraging hypothesis, which predicts that Lévy flights offer higher search efficiencies in environments where prey is scarce. Humphries et al.² show that marine predators often move in patterns that are consistent with this hypothesis.

(Do animals ever get lost?)