Cities and space: Common power laws and spatial fractal structures

TL;DR

This paper investigates the spatial distribution of cities within countries, revealing power law patterns and fractal structures that suggest an inherent hierarchical organization in urban systems across multiple nations.

Contribution

It demonstrates that city distributions at various spatial scales follow power laws and exhibit fractal properties, using data from six countries and novel spatial hierarchy constructions.

Findings

Large cities are more spaced out than random chance predicts.

City size distributions in spatial hierarchies follow power laws.

Spatial fractal structures are evident across different countries.

Abstract

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 US, 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.