基于空间填充间断性的中心位置分形系统
Fractal Systems of Central Places Based on Intermittency of Space-filling
摘要：
中心地模型在理论地理学和城市规划理论中具有重要意义。中心地网络的结构和质地在理论和实证研究中都被证明是自相似的。然而，迄今为止，中心地分形在现实世界中的基本原理尚未被揭示。本文旨在阐明中心地系统产生分形图案的机制。传统中心地模型的结构维数为d=2，说明人居环境空间分布不具有连续性。这个维度值与经验观察不一致。用不完全空间填充代替完全空间填充，我们可以得到分数维D<d=2的中心位置模型，其指示空间不连续性。从而将传统的中心地模型转化为分形中心地模型。如果在改进后的中心地分形中进一步引入机会因子，该理论将能更好地解释城市空间的真实格局。作为实证分析，美国的城市和城镇被用来验证基于分形的中心地模型。
英文摘要：
The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies. However, the underlying rationale of central place fractals in the real world has not yet been revealed so far. This paper is devoted to illustrating the mechanisms by which the fractal patterns can be generated from central place systems. The structural dimension of the traditional central place models is d=2 indicating no intermittency in the spatial distribution of human settlements. This dimension value is inconsistent with empirical observations. Substituting the complete space filling with the incomplete space filling, we can obtain central place models with fractional dimension D<d=2 indicative of spatial intermittency. Thus the conventional central place models are converted into fractal central place models. If we further integrate the chance factors into the improved central place fractals, the theory will be able to well explain the real patterns of urban places. As empirical analyses, the US cities and towns are employed to verify the fractal-based models of central places.
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