2012/09/27 by Yanguang Chen, Jian Feng · 18 citations
Earth and Planetary Sciences · Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Affine transformation #Demography #Exponential function #Fractal #Fractal dimension #Geometry #Land Use and Ecosystem Services #Mathematical analysis #Mathematics #Physics #Population #Probability density function #Remote Sensing and Land Use #Scaling #Statistical physics #Statistics #Urban Design and Spatial Analysis #physics.soc-ph
paper · pdf · doi:10.1016/j.chaos.2012.07.010
published in Chaos Solitons & Fractals 45(11), 1404-1416 (Elsevier BV)
openalex publication_date 2012/09/27 · arxiv created 2016/06/14 · arxiv updated 2016/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Urban population density always follows the exponential distribution and can be described with Clark's model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark's model differs from the exponential function in mathematics because that urban population is distributed on the fractal support of landform and land-use form. By using mathematical transform and empirical evidence, we argue that there are self-affine scaling relations and local power laws behind the exponential distribution of urban density. The scale parameter of Clark's model indicating the characteristic radius of cities is not a real constant, but depends on the urban field we defined. So the exponential model suggests local fractal structure with two kinds of fractal parameters. The parameters can be used to characterize urban space filling, spatial correlation, self-affine properties, and self-organized evolution. The case study of the city of Hangzhou, China, is employed to verify the theoretical inference. Based on the empirical analysis, a three-ring model of cities is presented and a city is conceptually divided into three layers from core to periphery. The scaling region and non-scaling region appear alternately in the city. This model may be helpful for future urban studies and city planning.