2011/04/16 by Yanguang Chen · 13 citations
Economics, Econometrics and Finance · Environmental Science · Mathematics · Physics and Astronomy · Social Sciences · #Computer science #Human Mobility and Location-Based Analysis #Land Use and Ecosystem Services #Law #Mathematical economics #Mathematics #Political science #Regional Economics and Spatial Analysis #Shuffling #Statistics #Zipf's law #physics.soc-ph
paper · pdf · doi:10.1155/2012/480196
published in Discrete Dynamics in Nature and Society 2012(1) (Hindawi Publishing Corporation) · 28 pages, 8 figures
arxiv created 2011/04/16 · openalex publication_date 2012/01/01 · openalex created_date 2016/06/24 · arxiv updated 2018/12/21 · openalex updated_date 2026/08/05
Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world and social institutions. Where there is a hierarchy with cascade structure, there is a Zipf′s rank‐size distribution, and vice versa . However, we have no theory to explain the spatial dynamics associated with Zipf′s law of cities. In this paper, a new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random distribution of cities. The hierarchical structure can be described with a set of exponential functions that are identical in form to Horton‐Strahler′s laws on rivers and Gutenberg‐Richter′s laws on earthquake energy. From the exponential models, we can derive four power laws including Zipf′s law indicative of fractals and scaling symmetry. A card‐shuffling model is built to interpret the relation between Zipf′s law and hierarchy of cities. This model can be expanded to illuminate the general empirical power‐law distributions across the individual physical and social sciences, which are hard to be comprehended within the specific scientific domains. This research is useful for us to understand how complex systems such as networks of cities are self‐organized.