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Spatial patterns and processes of cities can be described with variousentropy functions. However, spatial entropy always depends on the scale ofmeasurement, and it is difficult to find a characteristic value for it. Incontrast, fractal parameters can be employed to characterize scale-freephenomena. This paper is devoted to exploring the similarities and differencesbetween spatial entropy and fractal dimension in urban description. Drawing ananalogy between cities and growing fractals, we illustrate the definitions offractal dimension based on different entropy concepts. Three representativefractal dimensions in the multifractal dimension set are utilized to makeempirical analyses of urban form of two cities. The results show that theentropy values are not determinate, but the fractal dimension value is certain;if the linear size of boxes is small enough (e.g., <1/25), the linearcorrelation between entropy and fractal dimension is clear. Further empiricalanalysis indicates that fractal dimension is close to the characteristic valuesof spatial entropy. This suggests that the physical meaning of fractaldimension can be interpreted by the ideas from entropy and scales and theconclusion is revealing for future spatial analysis of cities. Key words:fractal dimension; entropy; mutlifractals; scaling; urban form; Chinese cities

Understanding Fractal Dimension of Urban Form through Spatial Entropy