Multiscalar Structures in Geography: Contributions of Scale Relativity

Abstract

Scale issues are very meaningful in geography, but nowadays nobody knows how to explain their ubiquitous existence theoretically. Fractality is not an accident for all geographical objects. The aim of this article is to demonstrate to what extent the theory of scale relativity (SR) can be used to solve the problem of geographic scales. With it, we can explain why fractal objects are everywhere. First, we summarize geographic scale position, followed by introducing all tools to understand SR with basic definitions, scale in cartography, how to measure a scale, scales in and from nature, and scale and theoretical geography. Second, we quickly describe the theory of SR. Indeed, it is an elementary geometry around first principles, characterization of scale variables, and scale laws. This article also aims to clarify why geographical objects are non-fractal, in a first calculus, and fractal, in a second calculus with the theory of scale relativity. Third, we will underpin this position through several geographic cases with a karstological example, two urban areas (Montéliard and Avignon), and a hydrographic network and contours of level lines (Gardons). All of them will be carefully analyzed with a fractal analysis. Therefore, we conclude that in this case we are well and truly within the framework of the theory of SR, depending on the results.