中心地系统的分形纹理与结构
Fractal Texture and Structure of Central Place Systems
摘要：
中心地模型的边界被证明是分形线，它们构成了中心地网络的分形结构。纹理分形可以用来解释边界线等区域边界的无标度性，但不能直接应用于实际人居环境系统的空间结构。针对这一问题，本文从纹理分形出发，研究了中心地模型的结构分形。该方法是基于分形集维数规则的理论推导。重建了中心位置模型的纹理分形，由纹理维数导出了结构维数，并用k数和g数表示了中心位置分形。根据中心地系统的分形维数，构造了三种结构分形模型。理论发现经典的中心地模型包括Koch雪花曲线和Sierpinski空间填充曲线，推论交通原理在城乡演变中起主导作用。结果表明，纹理分维可以转化为结构分维。后一个维度可以直接用来评价现实世界中的城乡居民点分布。因此，纹理分形可以间接地用来解释人类住区系统的发展。
英文摘要：
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines, but it cannot be directly applied to spatial structure of real human settlement systems. To solve this problem, this paper is devoted to deriving structural fractals of central place models from the textural fractals. The method is theoretical deduction based on the dimension rules of fractal sets. The textural fractals of central place models are reconstructed, the structural dimensions are derived from the textural dimensions, and the central place fractals are formulated by the k numbers and g numbers. Three structural fractal models are constructed for central place systems according to the corresponding fractal dimensions. A theoretical finding is that the classic central place models comprise Koch snowflake curve and Sierpinski space filling curve, and an inference is that the traffic principle plays a leading role in urban and rural evolution. The conclusion can be reached that the textural fractal dimensions can be converted into the structural fractal dimensions. The latter dimensions can be directly used to appraise urban and rural settlement distributions in the real world. Thus, the textural fractals can be indirectly utilized to explain the development of the systems of human settlements.
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