城市形态的分维估算与分形判定

发布时间：2018-04-10 12:17

本文选题：城市形态 + 分形　；参考：《地理科学进展》2017年05期

【摘要】：城市形态的分形是城市发育到一定阶段涌现出的有序格局和复杂结构,其基本特征是空间分布的无尺度性质。当研究者基于某个显著性水平推断城市分维存在时,实际上就是基于相应的置信度判断分形特征。虽然分形城市研究已经多年,但大量有关维数测算的基础问题依然悬而未决。本文根据分形几何学的基本思想论证城市形态分维测算的若干问题。分维测量的准则是最佳覆盖——不多不少、恰到好处的覆盖。盒子覆盖是最容易理解的测量方法。采用盒子覆盖法测量城市形态分维时,应考虑三个标准:一是快速逼近,二是简便操作,三是稳定拟合。直观估计分维的办法是利用双对数坐标图。由于城市形态不是严格意义的分形,而是类似于文献中的"前分形",测量尺度与相应测度的幂律关系通常仅在一定尺度范围内有效,从而形成所谓标度区。本文围绕城市形态的分维测量和分形判断开展一系列讨论,包括尺度选取、标度区识别和统计标准等问题,对今后城市分形研究具有理论启示和方法论的参考价值。
[Abstract]:The fractal of urban form is an orderly pattern and complex structure that emerges in a certain stage of urban development, and its basic characteristic is the scale-free nature of spatial distribution.When researchers infer the existence of urban fractal dimension based on a significant level, it is actually based on the corresponding confidence level to judge fractal features.Although fractal cities have been studied for many years, a large number of basic problems related to dimension calculation are still unresolved.Based on the basic idea of fractal geometry, this paper discusses some problems in calculating the fractal dimension of urban morphology.The criterion of fractal dimension measurement is the best coverage-no more, no less, just the right coverage.Box coverage is the most easily understood method of measurement.Three criteria should be considered when measuring fractal dimension of urban morphology by box covering method: one is fast approaching, the other is simple operation, and the third is stable fitting.The method of intuitionistic estimation of fractal dimension is to use the double logarithmic coordinate graph.Since urban morphology is not a strict fractal, but is similar to the "pre-fractal" in the literature, the power-law relationship between the measurement scale and the corresponding measure is usually only valid within a certain scale range, thus forming the so-called scale area.In this paper, a series of discussions on fractal dimension measurement and fractal judgment of urban morphology are carried out, including the selection of scale, the identification of scale areas and statistical standards, etc., which have theoretical enlightenment and reference value of methodology for the future study of urban fractal.
【作者单位】：北京大学城市与环境学院;
【基金】：国家自然科学基金项目(41671167)~~
【分类号】：C912.81;O189

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