A New Model of Urban Population Density Indicating Latent Fractal Structure

TL;DR

This paper introduces a novel model for analyzing urban population density that reveals hidden fractal structures, aiding understanding of urban form complexity and evolution.

Contribution

It proposes a new approach using the generalized gamma function to estimate latent fractal dimensions in urban density distributions.

Findings

Urban form evolves from simple to complex structures over time.

The model successfully estimates fractal dimensions in complex urban patterns.

Application to Hangzhou demonstrates the method's effectiveness.

Abstract

Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal cities, we need the measure of fractional dimension. However, if the fractal organization is concealed in the complex spatial distributions of geographical phenomena, the common methods of evaluating fractal parameter will be disabled. In this article, a new model is proposed to describe urban density and estimate fractal dimension of urban form. If urban density takes on quasi-fractal pattern or the self-similar pattern is hidden in the negative exponential distribution, the generalized gamma function may be employed to model the urban landscape and estimate its latent fractal dimension. As a case study, the method is applied to the city of Hangzhou, China. The results show that urban form evolves from simple to complex structure with time.