PROGRESS IN GEOGRAPHY ›› 2019, Vol. 38 ›› Issue (1): 50-64.doi: 10.18306/dlkxjz.2019.01.005

• Specical Column: Coordinated Development of the Beijing-Tianjin-Hebei Region • Previous Articles     Next Articles

Multifractal spectral analysis of land use structure of the Beijing-Tianjin-Hebei urban system

Linshan HUANG(), Yanguang CHEN*(), Shuangcheng LI   

  1. Department of Urban and Economic Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China
  • Received:2018-03-07 Revised:2018-07-20 Online:2019-01-28 Published:2019-01-22
  • Contact: Yanguang CHEN;
  • Supported by:
    Major Program of National Natural Science Foundation of China, No. 41590843.


Cities and urban systems both bear scale-free properties, from which no characteristic scales can be found for mathematical modeling and quantitative analysis. Therefore, fractal geometry is useful for making scaling analysis. Complex urban systems cannot be effectively described by simple fractal models, but can be characterized by multifractal theory. This paper is devoted to exploring the spatiotemporal features of urban change in the Beijing-Tianjin-Hebei region from 1995 to 2013. Using multifractal parameter spectrums, we can reveal the spatial dynamics of urbanization from the aspects of urban form and urban system. The main findings are as below: 1) The spectral curves of global fractal dimension are abnormal. If q>1 and q→∞, the spectral lines quickly converge to horizontal lines; when q<0 and q→-∞, the spectral lines quickly surpass the upper limit of fractal dimension, 2, which represents Euclidean dimension of embedding space. 2) The spectral curves of local fractal dimension are also not entirely normal. The peaks of the f(α) curves incline to the left, and the left ends of the curves are higher than the right ends. The problem lies in that the curves go beyond the maximum value of 2. 3) Fractal dimension growth curves can be described by the quadratic logistic function. Capacity parameters and inflection points of different fractal dimension growth curves are different. The main conclusions are as follows: 1) The urban fringes are disorderly developed, while the central areas of the main cities in the Beijing-Tianjin-Hebei region is overfilled with construction land, leaving little buffer space. 2) The main mode of urban growth is to expand to the outside region, but there are signs of central agglomeration in the total construction land of Hebei Province. 3) Land use of the main cities is close to saturation, and the speed of land expansion has peaked for Beijing and Tianjin, but not in Hebei Province yet. In short, it is necessary to optimize the land use structure in the Beijing-Tianjin-Hebei region by city planning.

Key words: urban system, multifractals, multifractal dimension spectrum, self-affinity, land use, Beijing-Tianjin-Hebei region