Evaluation of the Heterogeneous Spatial Distribution of Population and Stores/Facilities by Multifractal Analysis - Ito, Mariko I.; Ohnishi, Takaaki (Frontiers in Physics, 2020)
The spatial distribution of a population is not homogeneous—some areas attract many residents, while others do not. The spatial distribution of stores and facilities that have been coevolving with that of the population is also heterogeneous. Previous studies have shown that multifractality is a characteristic of the spatial distribution of a population, as well as other quantities associated with the urban system. We found that stores/facilities belonging to some categories also exhibit multifractality in spatial distribution. We quantified the spatial distributions of the population and stores/facilities in each category by multifractal analysis and compared their multifractal properties. Multifractal measures that reflect the heterogeneity of the densities in each location were able to capture additional features that cannot be seen when only the box-counting dimension was observed. Further, high concentrations of stores/facilities in categories relating to professional or commercial businesses were observed, consistent with previous studies on the scaling law, another pattern observed in urban morphology. We discuss the implications of the multifractal properties on the arrangement of locations where stores/facilities are concentrated. We believe that multifractal analysis is a powerful tool for the quantification of spatial distributions and expect that our interpretation of multifractal measures will stimulate further investigations into urban morphology.