The 3D Multifractal Characteristics of Urban Morphology in Chinese Old Districts

The compactness, diversity, and nested structures of the old districts in Chinese cities, in terms of their three-dimensional (3D) morphology, are particularly distinctive. However, existing multifractal measurement methods are insufficient in revealing these 3D structures. This paper introduces a 3D multifractal approach based on generalized dimension and Rényi entropy. In particular, a local indicator τq(h) is introduced for the analysis of the mapping of 3D units, with the Nanjing Old City serving as a case study. The results indicate the following: (1) The significant fractal characteristics of the Nanjing Old City, with a capacity dimension value of 2.344, indicating its limited 3D spatial occupancy. (2) The fluctuating generalized dimension spectrum ranges from 2.241 to 2.660, which differs from previous studies, suggesting that the 3D morphology does not exhibit typical multifractal characteristics. (3) The 3D map matrix reveals a fragmented open space system, a heterogeneous distribution of high-rise buildings, and cross-scale variations in morphological heterogeneity. This 3D multifractal method aids urban planners in assessing critical issues such as the fragmentation, crowding, and excessive heterogeneity of urban morphology, providing a spatial coordination and scaling of these issues through the 3D map matrix and enhancing the discussion of the broader mechanisms influencing morphological characteristics.