Multifractal Characterization of Urban Form and Growth: The Case of Beijing

Urban form takes on properties similar to random growing fractals and can be described in terms of fractal geometry. However, a model of simple fractals is not effectual enough to characterize both the global and local features of urban patterns. In this paper multifractal measurements are employed to model urban form and analyze urban growth. The capacity dimension D 0 , information dimension D 1 , and correlation dimension D 2 of a city's pattern can be estimated utilizing the box-counting method. If D 0 > D 1 > D 2 significantly, the city can be treated as a system of multifractals, and two sets of fractal parameters, including global and local parameters, can be used to spatially analyze urban growth. In this case study, multifractal geometry was applied to Beijing city, China. The results based on the remote-sensing images taken in 1988, 1992, 1999, 2006, and 2009 show that the urban landscape of Beijing bears multiscaling fractal attributes. The dimension spectrum curves show several abnormal aspects, especially the upper limit of the global dimension breaks through the Euclidean dimension of embedding space and the local dimension fails to converge in a proper way. The geographical features of Beijing's spatiotemporal evolution are discussed, and the conclusions may be instructive for spatial optimization and city planning in the future.