A multifractal method based on Spacematrix type units for analysing cross-scale characteristics of urban morphology

The urban morphological system, developed over multiple phases, exhibits complex cross-scale characteristics, with significant scale discrepancies among morphological elements at the same hierarchical level, which suggests that the cross-scale sliding model holds the potential to reveal additional characteristics of urban morphology. This paper introduces a multifractal method that integrates Spacematrix morphological classification for the analysis of detailed urban building data within defined boundaries. Using the Nanjing Old City in China as a case study, the results reveal a dense yet balanced urban form, showing annular differentiation characterized by fragmented fringe belts at the macro level and a uniform mixture of diverse land use types and building types at the micro level. The typical scale invariance and multifractality are not consistently observed across single-type analyses. The study identifies height uniformization and spaciousness differentiation in the scaling of urban morphology, attributing the multifractal mechanism to the interweaving and transformation of multiple types across scales. This enhanced multifractal approach improves spatial mapping capabilities, aiding in the elucidation of the formation mechanisms of urban morphology.