  The growth curves of fractal dimension of urban form take on squashing effect
and can be described by sigmoid functions. The fractal dimension growth of
urban form in western countries can be modeled by Boltzmann's equation and
logistic function. However, these models cannot be well applied to the fractal
dimension growth curve of Beijing city, the national capital of China. In this
paper, the experimental method is employed to find parametric models for the
growth curves of fractal dimension of Chinese urban form. By statistical
analysis, numerical analysis, and comparative analysis, we find that the
quadratic Boltzmann equation and quadratic logistic function can be used to
characterize how the fractal dimension of the urban land-use pattern of Beijing
increases in the course of time. The models are also suitable for many cities
in the north of China. In order to convert the empirical models into
theoretical models, we attempt to construct a model of spatial replacement
dynamics of urban evolution, from which the logistic model of urban fractal
dimension growth can be derived. The models can be utilized to predict the rate
and upper limitation of Chinese urban growth. In particular, the models can be
employed to reveal the similarities and differences between the fractal growth
of Chinese cities and that of the cities in western countries.
