Common power laws for cities and spatial fractal structures

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 117; no. 12; pp. 6469 - 6475
• Main Authors: Mori, Tomoya, Smith, Tony E., Hsu, Wen-Tai
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 24-03-2020
• Subjects: Cities; Fractals; Hierarchies; Partitioning; Social Sciences; Urban planning; spatial hierarchy; fractal structure; city size; power law
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1913014117

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 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.