Abstract
Multifractal analysis offers a number of advantages to measure spatial economic segregation and inequality, as it is free of categories and boundaries definition problems and is insensitive to some shape-preserving changes in the variable distribution. We use two datasets describing Kyoto land prices in 1912 and 2012 and derive city models from this data to show that multifractal analysis is suitable to describe the heterogeneity of land prices. We found in particular a sharp decrease in multifractality, characteristic of homogenisation, between older Kyoto and present Kyoto, and similarities both between present Kyoto and present London, and between Kyoto and Manhattan as they were a century ago. In addition, we enlighten the preponderance of spatial distribution over variable distribution in shaping the multifractal spectrum. The results were tested against the classical segregation and inequality indicators, and found to offer an improvement over those.
Highlights
Reardon et al [1] pointed out the necessity for new spatial economic segregation and inequality measures insensitive to the choice of category thresholds, boundary definitions, and shapepreserving changes in the variable distribution
We have identified that the new measures proposed in the same article still face boundary definition biases and are unsatisfactorily insensitive to all changes in the variable distribution, including non shape-preserving ones
We first present a detailed analysis for Taisho era Kyoto and its associated models, a more concise analysis for present Kyoto due to the less appealing shape of the data
Summary
Reardon et al [1] pointed out the necessity for new spatial economic segregation and inequality measures insensitive to the choice of category thresholds, boundary definitions, and shapepreserving changes in the variable distribution. We have identified that the new measures proposed in the same article still face boundary definition biases (a common issue in spatial statistics usually referred to as the Modifiable Areal Unit Problem, or MAUP) and are unsatisfactorily insensitive to all changes in the variable distribution, including non shape-preserving ones. Multifractal analysis could offer a good alternative, free of all the aforementioned problems, for sets obeying a number of scaling conditions. It is well known that scaling often emerges in self-organized complex systems, and the fractality of urban structures in particular is well documented [2,3,4].
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