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Open AccessArticle

Spatial Measures of Urban Systems: from Entropy to Fractal Dimension

Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China
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Entropy 2018, 20(12), 991; https://doi.org/10.3390/e20120991
Received: 2 November 2018 / Revised: 29 November 2018 / Accepted: 14 December 2018 / Published: 19 December 2018
(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)
One type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimensions can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connection between entropy and fractal dimensions, they have different application scopes and directions in urban studies. This paper focuses on exploring how to convert entropy measurements into fractal dimensions for the spatial analysis of scale-free urban phenomena using the ideas from scaling. Urban systems proved to be random prefractal and multifractal systems. The spatial entropy of fractal cities bears two properties. One is the scale dependence: the entropy values of urban systems always depend on the linear scales of spatial measurement. The other is entropy conservation: different fractal parts bear the same entropy value. Thus, entropy cannot reflect the simple rules of urban processes and the spatial heterogeneity of urban patterns. If we convert the generalized entropies into multifractal spectrums, the problems of scale dependence and entropy homogeneity can be solved to a degree for urban spatial analysis. Especially, the geographical analyses of urban evolution can be simplified. This study may be helpful for students in describing and explaining the spatial complexity of urban evolution. View Full-Text
Keywords: entropy; fractal; scaling; scale dependence; spatial heterogeneity; urban land use entropy; fractal; scaling; scale dependence; spatial heterogeneity; urban land use
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Chen, Y.; Huang, L. Spatial Measures of Urban Systems: from Entropy to Fractal Dimension. Entropy 2018, 20, 991.

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