Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-Ku, Kyoto 606-8501, Japan;
Research Institute of Economy, Trade and Industry, Ministry of Economy, Trade, and Industry, Kasumigaseki Chiyoda-ku, Tokyo 100-8901, Japan.
Proc Natl Acad Sci U S A. 2020 Mar 24;117(12):6469-6475. doi: 10.1073/pnas.1913014117. Epub 2020 Mar 6.
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.
城市规模分布在广泛的国家范围内被认为可以很好地用幂律来近似。但是，这种分布在其他空间尺度上也是有意义的，例如在一个国家的某些地区内。利用来自中国、法国、德国、印度、日本和美国的数据，我们首先记录到，大城市之间的间隔明显比仅凭机会所预期的要大。接下来，我们通过首先使用给定数量的最大城市作为单元格中心来划分地理空间，然后在每个单元格内递归地继续此划分过程，为各国构建空间层次结构。我们发现，这些空间层次结构的不同部分中的城市规模分布表现出幂律，再次表明存在空间分形结构，而且这种相似性远远超过仅凭机会所预期的。
