Exploring the Structural Fractality of Urban Road Networks by Different Representations

Abstract

Organisms and other living things grow as fractals, helping to maximize space-filling ability and transmit flow efficiently. In recent years, many studies on fractals have been carried out, mostly at a geometric level, although little work has been done on fractal properties at a structural level. In fact, the capacity of geographical objects, especially road networks, is dependent not only on the geometric distribution described by a geometric fractal dimension but also on the level of structural complexity as described by a structural fractal dimension. Past studies on a structural fractal dimension are limited to a single scale and a single representation. Because different representations could lead to different results in fractal analysis, this study aims to examine the structural fractality of urban road networks by different representations. The road networks of the 100 most populous cities in the United States were examined by three commonly used topological representations. The following results were established: Despite differences in representation, structural fractality always exists; structural fractal dimensions in stroke-based representation are obviously larger than those in segment-based representation; and scale has no obvious effects on structural fractality. These results could deepen our understanding of how urban road networks evolve.

有机体和其它生物以分形的形式生长, 有助于最大限度地利用空间和高效的流动。近年来, 人们对分形进行了大量的研究, 但主要是在几何层面上, 而在结构层面上对分形特征的研究却很少。事实上, 地理对象（尤其是道路网）的容量, 不仅取决于几何分形所描述的几何分布, 还取决于结构分形所描述的结构复杂程度。以往对结构分形的研究仅限于单一尺度和单一表征。由于不同的表征会导致不同的分形分析结果, 本研究旨在探讨不同表征下城市道路网的结构分形。通过三种常用拓扑表征, 本文探讨了美国100个人口最多城市的道路网。结果表明：尽管在表征上存在着差异, 但结构分形始终存在；基于Stroke表征的结构分形明显大于基于路段表征的结构分形；尺度对结构分形的影响不明显。这些结果可以加深我们对城市道路网演变的理解。

Los organismos y diversos seres vivos crecen como fractales, ayudando a maximizar la capacidad de llenar espacio y transmitir flujo eficientemente. En años recientes, se han llevado a cabo muchos estudios sobre fractales, en la mayoría de los casos a nivel geométrico, aunque muy poco trabajo se ha adelantado sobre las propiedades de los fractales a nivel estructural. De hecho, la capacidad de los objetos geográficos, especialmente las redes de carreteras, descansa no solo en la distribución geométrica descrita por una dimensión geométrica fractal, sino también en el nivel de la complejidad estructural, según se la describe por una dimensión fractal estructural. Los estudios anteriores sobre la dimensión fractal estructural están restringidos a una escala sencilla y a una representación sencilla. Por cuanto diferentes representaciones podrían conducir a resultados diferentes en el análisis fractal, este estudio apunta a examinar la fractalidad estructural de las redes de carreteras urbanas por representaciones diferentes. Se examinaron las redes de carreteras de las 100 ciudades más populosas de los Estados Unidos, con tres representaciones topológicas comúnmente usadas. Se establecieron los siguientes resultados: A pesar de las diferencias en la representación, la fractalidad estructural siempre existe; las dimensiones fractales estructurales en la representación basada en golpes son obviamente más grandes que las de representación basada en segmentos; y la escala no tiene efectos obvios sobre la fractalidad estructural. Estos resultaos podrían profundizar nuestra comprensión sobre el modo como evolucionan las redes de carreteras urbanas.

Key Words:

• dual representation
• primal representation
• road network
• scale effect
• structural fractality

关键词:

• 双重表征
• 原始表征
• 道路网
• 尺度效应
• 结构分形。

Palabras clave:

• efecto de escala
• fractalidad estructural
• red de carreteras
• representación dual
• representación primaria

Acknowledgments

We thank the editor and the three anonymous reviewers for their constructive comments, which led to significant improvement in the quality of this article. We also thank Shan Xu and Yanyu Chen at Southwest Jiaotong University for helpful discussions. Chengliang Liu served as the corresponding author for this article.

Additional information

Funding

This work was supported by the Key Research and Development Program of Chengdu (2019-YF05-02119-SN), the Program of Science and Technology of Sichuan Province, China (2020YJ0325), and the Shanghai Philosophy and Social Science Project (2020BGL034).

Notes on contributors

Hong Zhang

HONG ZHANG is Associate Professor in the School of Urban and Regional Science, East China Normal University, Shanghai 200241, China. E-mail: [email protected]. Her research interests include spatial complexity, information theory, and urban geography.

Peichao Gao

PEICHAO GAO is Assistant Professor in the Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China. E-mail: [email protected]. His research interests include geospatial analysis, spatial information, and multi-objective optimization.

Tian Lan

TIAN LAN is a PhD Candidate in the Department of Land Surveying and Geo-Informatics, Hong Kong Polytechnic University, Hong Kong 99907, China. E-mail: [email protected]. His research interests include spatial optimization, geographical complexity analysis, and map generalization.

Chengliang Liu

CHENGLIANG LIU is Professor in the School of Urban and Regional Science, East China Normal University, Shanghai 200241, China. E-mail: [email protected]. His research interests focus on spatial complexity in transport geography and regional innovation networks.