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| ON FRACTAL DIMENSION CALCULATION AND ANALYSIS OF URBAN FORM |
| CHEN Yan-guang1, LIU Ji-sheng2 |
1. Department of Geography, Peking University, Beijing 100871, China;
2. Department of Geography, Northeast Normal University, Changchun 130024, China |
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Abstract 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.
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Received: 28 June 2006
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2007, Vol. 22 
