Cities and space: Common power laws and spatial fractal structures
Abstract
City size distributions are known to be well approximated by powerlaws across a wide range of countries. But such distributions arealso 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 ascell centers, and then continuing this partitioning procedure withineach cell recursively. We find that city size distributions in differentparts of these spatial hierarchies exhibit power laws that are again farmore similar than would be expected by chance alone – suggestingthe existence of a spatial fractal structure.