A classification-based multifractal analysis method for identifying urban multifractal structures considering geographic mapping

Identifying urban multifractal structures are helpful for understanding urban spatial organization patterns as complex systems. Multifractal analysis is a powerful tool to model multifractal structures. However, due to the use of statistical moments to delineate the multifractal spectrum for multifractal analysis, the great majority of existing studies cannot map urban multifractal structures to geographic space. Lack of geographic mapping makes it difficult to interpret the causes of the anomalous scaling characteristics of urban multifractal structures. For the few mappable multifractal structure modeling methods, they model multifractal structures from a global or local perspective that generates inadequate or redundant scaling characteristics. Here, a classification-based multifractal analysis method (CMFA) was proposed to overcome the shortcomings. It classifies the urban areas into zones according to the density of urban elements and builds up the multi-scaling relationships of urban elements for each zone. The corresponding multifractal structures can be mapped according to the spatial distribution of zones across scales. A case study was conducted to identify the multifractal structures of nighttime light in Beijing, China, to verify the CMFA method. In conclusion, when there are abnormal scaling characteristics reflected by the multifractal spectrum, the multifractal structure maps can diagnose the land use problems leading to disordered spatial organization patterns. Urban planners should focus on such problem land parcels and carry out urban renewal to optimize urban spatial structures.