LOGISTIC MODELS OF FRACTAL DIMENSION GROWTH OF URBAN MORPHOLOGY

Abstract

Urban form can be described with fractal dimension, which is a measurement of space filling of urban evolution. However, how to model and understand the fractal dimension growth of urban morphology are still pending questions. This paper is devoted to the research on the fractal dimension curves of urban growth. The principle of squashing function and empirical evidences are employed to demonstrate the following inference: the fractal dimension time series of a city’s spatial form take on a sigmoid curve. Among various sigmoid functions, the logistic function is the most probable selection. The observational data of fractal dimension of different cities from different sources support this logic judgment. A further discovery is that the fractal dimension curves of cities in the developed countries differ from those in the developing countries. A generalized logistic function is thus proposed to model the fractal dimension curves of different types of cities. The general logistic models can be used to predict the missing values and estimate the growth rates of fractal dimension of city development. Moreover, these models can be utilized to analyze when and where there is a fractal of urban form.