The European Physical Journal E ( IF 1.8 ) Pub Date : 2021-07-17 , DOI: 10.1140/epje/s10189-021-00100-2 Andy M Reynolds 1
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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.
Graphic abstract
中文翻译：
Weierstrassian Lévy 步行是爬行的副产品
摘要
Weierstrassian Lévy 游走是最简单的随机游走之一，它不满足中心极限定理并且已经成为尺度不变性的缩影，尽管它们最初被认为是一种数学抽象。在这里，我展示了这些 Lévy 步行是如何作为爬行的副产品产生的，爬行是一种常见但古老的运动形式。这或许可以解释为什么 Weierstrassian Lévy 步法能够准确描述不同种类的软体动物——某些贻贝、泥螺和帽贝——的运动模式。我表明这种运动不是软体动物特有的，因为它们在果蝇中也很明显幼虫。这些发现进一步加深了人们的认识，即有许多特殊的、看似偶然的路径可以通往 Lévy 步行。并且 Lévy 游走的发生不需要归因于有利的搜索策略的执行。
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