Describing urban evolution with the fractal parameters based on area-perimeter allometry

TL;DR

This paper improves the measurement of urban fractal parameters using area-perimeter allometry, revealing that local and global parameters are closely related, and demonstrates this approach with a case study of cities in China's Yangtze River Delta.

Contribution

It introduces an adjusted formula for more accurate boundary dimension estimation and integrates form and boundary dimensions to better characterize urban structure and evolution.

Findings

Local fractal parameters approximate global parameters, indicating they are decompositions.

The integrated fractal parameters effectively characterize urban form and texture.

The method is applicable to low-resolution remote sensing images.

Abstract

The area-perimeter allometric scaling is a basic and important approach for researching fractal cities and has been studied for a long time. However, the boundary dimension of a city is always numerically overestimated by the traditional formula. An adjusting formula has been derived to revise the overestimated boundary dimension and estimate the form dimension, but the association between the global and local fractal parameters is not clear. This paper is devoted to describing the urban evolution by using the improved fractal parameters based on the area-perimeter measure relation. A system of 68 cities and towns in Yangtze River Delta, China, is taken as an example to make a case study. A discovery is that the average values of the local fractal parameters are approximately equal to the corresponding global fractal parameters of cities. This suggests that the local parameters are the decomposition of the global parameters. The novelty of this empirical study is as follows: first, the form dimension and boundary dimension are integrated to characterize the urban structure and texture; second, the global and local parameters are combined to characterize an urban system and individual cities. By illustrating how to carry out the area-perimeter scaling analysis in the case of remote sensing images with low resolution, this work suggests a possible new approach to researching fractal systems of cities.