Common power laws for cities and spatial fractal structures

Tomoya Mori, Tony E. Smith, Wen-Tai Hsu
2020 Proceedings of the National Academy of Sciences of the United States of America  
City-size distributions are known to be well approximated by power laws across a wide range of countries. But such distributions are also meaningful at other spatial scales, such as within certain regions of a country. Using data from China, France, Germany, India, Japan, and the United States, we first document that large cities are significantly more spaced out than would be expected by chance alone. We next construct spatial hierarchies for countries by first partitioning geographic space
more » ... geographic space using a given number of their largest cities as cell centers and then continuing this partitioning procedure within each cell recursively. We find that city-size distributions in different parts of these spatial hierarchies exhibit power laws that are, again, far more similar than would be expected by chance alone—suggesting the existence of a spatial fractal structure.
doi:10.1073/pnas.1913014117 pmid:32144142 fatcat:ymmugavpuvdl3fdnb5c6ksl23q