Spatial Distribution of Human Population in France: Exploring the Modifiable Areal Unit Problem Using Multifractal Analysis

Case studies in geography are strongly dependent on the size of the spatial units used for the analysis. This has been expressed as the Modifiable Areal Unit Problem (MAUP): whatever the phenomenon under consideration, it is impossible to identify a single spatial partition that would be most appropriate to analyze it. In this respect, multifractal analysis may be an interesting tool for geographers. It integrates not just a series of nested spatial resolutions, as fractal analysis does, but also a series of points of view about the quantity of information contained in each spatial unit. In this article, we first expose the mathematical bases of multifractal analysis and we describe how it applies to geographical analyses. We insist on the mathematical notion of dimension, which allows us to describe how multifractal parameters can be used to quantify the MAUP. Then, we use the method to characterize the spatial distribution of population density in France. The main result is a typology map of population density that uses the MAUP as a descriptive tool. This map allows the joint identification of several phenomena: the main cities, the rural settlement patterns, and several types of periurban settlement patterns.