Multifractal Structures and the Energy-Economic Efficiency of Chinese Cities: Using a Classification-Based Multifractal Method

Improper urban spatial structure can lead to problems such as traffic congestion, long commuting times, and diseconomies of scale. Evaluating the efficiency of urban spatial structure is an important means to enhance the sustainable development of cities. The fractal method has been widely used in the identification and efficiency evaluation of urban spatial structure due to its sufficient characterization of urban complexity. However, the identification of urban fractal structures has expanded from monofractal structures to multifractal structures, while the efficiency evaluation of urban fractal structures remains limited to the single-dimensional efficiency evaluations of single fractals, seriously affecting the reliability of urban fractal structure evaluation. Therefore, this study identifies and evaluates urban spatial structure within the unified framework of multifractal analysis. Specifically, a classification-based multifractal method is introduced to identify the multifractal structure of 290 cities in China. An iterative application of the geographic detector method is used to evaluate the comprehensive energy-economic efficiency of urban multifractal structures. The results indicate that the 290 Chinese cities include 6 typical multifractal structures. The explanatory power of these six typical multifractal structures for urban energy-economic efficiency is 16.27%. The advantageous multifractal structures of cities that achieve higher energy-economic efficiency rates satisfy a cubic polynomial form. By comparing them with the advantageous multifractal structures, the main problems affecting the efficiency of urban multifractal structures in the other five types of cities are shown to include overly strong or weak concentration capacity of high-level centers, weak hierarchical structures among centers, and the spreading of low-level centers.