Weierstrassian Lévy walks are a by-product of crawling.

Abstract

Weierstrassian Lévy walks are one of the simplest random walks which do not satisfy the central limit theorem and have come to epitomize scale invariance even though they were initially regarded as being a mathematical abstraction. Here, I show how these Lévy walks can be generated intrinsically as a by-product of crawling, a common but ancient form of locomotion. This may explain why Weierstrassian Lévy walks provide accurate representations of the movement patterns of a diverse group of molluscs-certain mussels, mud snails and limpets. I show that such movements are not specific to molluscs as they are also evident in Drosophila larvae. The findings add to the growing realization that there are many idiosyncratic, seemingly accidental pathways to Lévy walking. And that the occurrence of Lévy walks need not be attributed to the execution of an advantageous searching strategy.