2026年 第3期 DOI：10.19830/j.upi.2024.296
基于多分形矩阵映射的城市中心区形态跨尺度研究
Cross-scale Research on the Morphology of Urban Central District Based on Multifractal Matrix Mapping
张晨阳 杨俊宴 王暄晴 邵典
ZHANG Chenyang, YANG Junyan, WANG Xuanqing, SHAO Dian
关键词：城市形态；城市中心区；跨尺度；多分形；密度
Keywords：urban morphology; urban central district; cross-scale; multifractal; density
摘要：城市中心区形态在长期发展中形成了没有特征尺度的整体系统。多分形方法虽有助于从维数和谱形方面揭示其形态系统复杂的密度特征，但也存在空间映射能力不足的问题。本文首先在跨尺度的整体视角下，梳理出多分形特征所对应的城市形态学关键议题；其次以南京老城范围的建筑平面形态为例，构建了基于广义关联维数（容量、信息、关联、谱形）的测度方法，以及基于尺度和矩阶的矩阵映射分析方法。研究结果显示：南京老城建筑形态呈现出集聚的扁平化组织结构，开放空间形态呈现出跨尺度断裂的孔隙状结构；宏观尺度下，低密度区域表现出结构消散特征，高密度区域表现出带状凝聚特征，过渡区域表现出边缘化退散特征。本研究拓展了城市形态学的研究工具，提升了多分形算法对具体空间区域的分析能力，有助于揭示城市形态在尺度和密度方面的复杂性特征。
Abstract：The morphology of urban district areas has developed into a comprehensive system without a characteristic scale over the long term. The multifractal method helps to reveal the complex density characteristics of morphology systems in terms of dimensionality and spectral shape. However, the multifractal method also faces challenges regarding its spatial mapping capabilities. From a cross-scale holistic perspective, this paper elucidates the key issues of urban morphology research corresponding to multifractal features. Using the architectural plan form of Nanjing old city area as an example, this paper develops measurement techniques grounded in the concepts of capacity, information, correlation, and spectral shape within the framework of generalized correlation dimension. Additionally, it employs matrix mapping analysis methods that integrate scale and statistical moments. The research results indicate that the architectural morphology of the Nanjing old city area exhibits an aggregated and flattened organizational structure, while the open space morphology presents a cross-scale fractured porous structure. At the macro scale, low-density areas exhibit structural dissipation characteristics, high-density areas exhibit strip-like aggregation characteristics, and transition areas exhibit marginal dispersion characteristics. This study expands the research tools of urban morphology and enhances the analytical capabilities of multifractal algorithms for specific spatial regions, helping to reveal the complexity of urban morphology in terms of scale and density.
版权信息：
基金项目：国家自然科学基金重大项目“高密度城市环境碳中和建筑技术原型构建”（52394422015），国家自然科学基金青年基金“基于‘数—形’双通量图谱的高密度街区形态测度模型与交互转译方法研究”（52308051）
作者简介：张晨阳，东南大学建筑学院，博士研究生。zhangchenyang@tongji.edu.cn
杨俊宴（通信作者），博士，东南大学建筑学院，首席教授、博士生导师；东南大学智慧城市研究院，副院长。yangjy_seu@163.com
王暄晴，东南大学建筑学院，硕士研究生。wangxq0122@163.com
邵典，东南大学建筑学院，博士后。101300274@seu.edu.cn