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 3...
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MDPI AG
2025-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/3/195 |
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| author | Chenyang Zhang Junyan Yang Xinzhe Liu Dian Shao Zhonghu Zhang Zhihan Zhang Haocheng Sun Yuyue Huang Daijun Chen Xun Zhang |
| author_facet | Chenyang Zhang Junyan Yang Xinzhe Liu Dian Shao Zhonghu Zhang Zhihan Zhang Haocheng Sun Yuyue Huang Daijun Chen Xun Zhang |
| author_sort | Chenyang Zhang |
| collection | DOAJ |
| description | 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 <i>τ<sub>q</sub></i>(<i>h</i>) 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. |
| format | Article |
| id | doaj-art-71844bd4242b4f7db3180e09fde78e35 |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-71844bd4242b4f7db3180e09fde78e352025-08-20T02:42:30ZengMDPI AGFractal and Fractional2504-31102025-03-019319510.3390/fractalfract9030195The 3D Multifractal Characteristics of Urban Morphology in Chinese Old DistrictsChenyang Zhang0Junyan Yang1Xinzhe Liu2Dian Shao3Zhonghu Zhang4Zhihan Zhang5Haocheng Sun6Yuyue Huang7Daijun Chen8Xun Zhang9School of Architecture, Southeast University, Nanjing 210096, ChinaSchool of Architecture, Southeast University, Nanjing 210096, ChinaSchool of Architecture, Southeast University, Nanjing 210096, ChinaSchool of Architecture, Southeast University, Nanjing 210096, ChinaSchool of Architecture, Southeast University, Nanjing 210096, ChinaSchool of Architecture, Southeast University, Nanjing 210096, ChinaSchool of Architecture, Southeast University, Nanjing 210096, ChinaSchool of Architecture, Southeast University, Nanjing 210096, ChinaSchool of Architecture, Southeast University, Nanjing 210096, ChinaSchool of Architecture, Southeast University, Nanjing 210096, ChinaThe 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 <i>τ<sub>q</sub></i>(<i>h</i>) 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.https://www.mdpi.com/2504-3110/9/3/195multifractalurban morphology3D fractalbox-counting analysisold district |
| spellingShingle | Chenyang Zhang Junyan Yang Xinzhe Liu Dian Shao Zhonghu Zhang Zhihan Zhang Haocheng Sun Yuyue Huang Daijun Chen Xun Zhang The 3D Multifractal Characteristics of Urban Morphology in Chinese Old Districts Fractal and Fractional multifractal urban morphology 3D fractal box-counting analysis old district |
| title | The 3D Multifractal Characteristics of Urban Morphology in Chinese Old Districts |
| title_full | The 3D Multifractal Characteristics of Urban Morphology in Chinese Old Districts |
| title_fullStr | The 3D Multifractal Characteristics of Urban Morphology in Chinese Old Districts |
| title_full_unstemmed | The 3D Multifractal Characteristics of Urban Morphology in Chinese Old Districts |
| title_short | The 3D Multifractal Characteristics of Urban Morphology in Chinese Old Districts |
| title_sort | 3d multifractal characteristics of urban morphology in chinese old districts |
| topic | multifractal urban morphology 3D fractal box-counting analysis old district |
| url | https://www.mdpi.com/2504-3110/9/3/195 |
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