Fractal Dimensions Derived from Spatial Allometric Scaling of Urban Form

TL;DR

This paper explores how fractal dimensions derived from spatial allometry can characterize urban form, revealing that traffic networks exhibit higher fractal dimensions than nodes and that these dimensions reflect correlation rather than capacity.

Contribution

It introduces a method to derive fractal dimensions from urban spatial allometry, providing new insights into urban system scaling and fractal properties.

Findings

Fractal dimensions of traffic lines are higher than those of traffic nodes.

Dimensions based on variable boundaries are lower than those based on concentric circles.

Fractal dimensions from spatial allometry are correlation dimensions, not capacity dimensions.

Abstract

The improved city clustering algorithm can be used to identify urban boundaries on a digital map, and the results are a set of isolines. The relationships between the urban measurements within the variable boundaries follow allometric scaling law, which indicates spatial allometry of cities. This paper is devoted to exploring the fractal dimension proceeding from urban spatial allometry. By theoretical reasoning and empirical analysis of urban traffic network, we can derive a set of fractal dimension from the spatial allometry and reveal the basic property of the new fractal parameters. The findings are as follows. First, the fractal dimension values of traffic lines are higher than those of traffic nodes. Second, the fractal dimension values based on variable boundaries are lower than those based on the concentric circles. Conclusions can be reached that the fractal dimensions coming from spatial allometry are a type of correlation dimension rather than capacity dimension, and the relative growth rate of traffic points is greater than that of traffic nodes. This study provides new way of understanding allometry, fractals, and scaling in urban systems.