Multifractal portrayal of the Swiss population

Abstract

Fractal geometry is a fundamental approach for describing the complex irregularities of the spatial structure of point patterns. The present research characterizes the spatial structure of the Swiss population distribution in the three Swiss geographical regions (Alps, Plateau and Jura) and at the entire country level. The analyses were carried out by means of a fractal measure (the box-counting dimension) and two multifractal measures (the Rényi generalized dimensions and the multifractal spectrum) for point patterns, which enabled the estimation of the spatial degree of clustering of a distribution at different scales. The Swiss population dataset is presented on a grid of points and thus it can be modelled as a realization of a "point process" where each point is characterized by its spatial location (geometrical support) and a number of inhabitants (measured variable). Results showed that the four patterns are multifractals and their population distribution present different clustering behaviours. Thus, applying multifractal and fractal methods at different geographical regions and at different scales allowed us characterising the degree of clustering of the population distribution in Switzerland and quantifying their dissimilarities. This paper is the first Swiss geodemographic study applying multifractal methods using high resolution data.

Keywords

• fractal dimension
• Rényi dimensions
• singularity spectrum
• geodemographics
• multifractal dimension
• box-counting