Modeling Growth Curve of Fractal Dimension of Urban Form of Beijing

TL;DR

This paper develops and validates quadratic Boltzmann and logistic models to accurately describe and predict the fractal dimension growth of Beijing's urban form, highlighting differences from Western cities.

Contribution

It introduces new quadratic parametric models for Chinese urban fractal growth and links empirical findings to a theoretical model of urban evolution.

Findings

Quadratic Boltzmann and logistic functions effectively model Beijing's fractal growth.

Models are applicable to other northern Chinese cities.

Theoretical model of urban evolution derived from empirical models.

Abstract

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.