城市形态分维测算和分析的若干问题

本文讨论了城市形态分维测算和分形分析的几个常见问题,这些问题常使初学者感到困惑。主要论述如下内容:分维的性质、特征和基本含义,无标度区的城市地理学意义、判断和界定方法以及城市演化分析中的作用,城市形态分维分析的一般步骤,分维与其他参量的关系,等等。作者强调,要想避免研究中出现的伪分形现象导致的错误结论,必须有效利用双对数坐标图识别反映自相似性尺度范围的无标度区。

ON FRACTAL DIMENSION CALCULATION AND ANALYSIS OF URBAN FORM

Measurement is the basic link between mathematics and empirical research. Since cities as fractals cannot be characterized with common measures such length, area, density, etc., the fractal dimension is of significance for the studies on urban form and structure. Several questions are discussed and made clear in this paper on calculation and analysis of fractal dimension of urban form. These questions always puzzle beginners in the field of city fractals or fractal cities. The solved problems are as followed. 1) The nature, property, and significance of fractal dimension. Fractal dimension is a set instead of a simple concept, including radius dimension based on rings, grid dimension based on lattices or boxes, boundary dimension based on geometrical measurement relations, etc. Different fractal parameters have different properties, different estimation methods, and can be applied to different objects for different purposes. A fittest dimension should be selected for urban form in given studies. 2) The geographical features and meanings of scale-free zone, within which self-similarity appears out. Fractal structure only appears in certain scale-free zone. It is shown that how to avoid "fractal rabbits" by using process of similar subdivision of triangle, and others. 3) The general process of analyzing fractal dimension. First, to determine an angle of view; Second, to estimate various fractal parameter values; Third, to analyze the fractal dimension values according to research objects; Fourth, to analyze the length of the scale-free zones. 4) The relationship between fractal dimension and other parameters on urban morphology, and so on. Fractal dimension can be related to other parameters associated with urban form, such as compactness ratio, circularity ratio, or even form ratio, etc. Fractal dimension is defined at the macro level, while the other parameters are defined at the micro level.