Derivation of the functional relations between fractal dimension of and shape indices of urban form

作者：Chen Yanguang^*

来源：Computers, Environment and Urban Systems, 2011, 35(6): 442-451.

DOI：10.1016/j.compenvurbsys.2011.05.008

• Urban form
• Urban shape
• City size
• City classification
• Fractal
• Boundary dimension
• Shape index
• Scaling range

The relationships between the size, scale, shape, and dimension of urban settlements are basic problems remained to be further resolved, and this paper provides an available perspective for understanding these problems. Based on the standard circle, the relations between the fractal dimension of urban boundary and the compactness ratios of urban shape were derived from a geometric measure relation in a simple way. The compactness ratios proved to be the exponential functions of the reciprocal of the boundary dimension. The results can be generalized and applied to the common indices of shape including circularity ratio, ellipticity index, and form ratio, which are defined by urban area, perimeter, or Feret's diameter. The mathematical models are empirically verified by the remote sensing data of China's 31 megacities in 1990 and 2000 and lend support to the assumption that urban boundaries are pre-fractals rather than real fractals. A conclusion can be drawn that there exist certain functional relations between the shape indices and the boundary dimension, and within certain range of scales, the fractal parameters can be indirectly estimated by the ratios of size measurements to reflect the features of urban shapes.

• 出版日期2011-11
• 单位北京大学