Urban Allometric Scaling Beneath Structural Fractality of Road Networks

Allometry originally referred to the scaling relationship between the size of a body part and the size of the whole body when an organism grows. Gradually, researchers introduced it into urban studies. In existing urban studies, many allometric relations were discovered, especially those between urban population and other (physical or socioeconomic) quantities, such as urban area and gross domestic product (GDP). Recently, geometric fractal dimension () was used as a complexity measure of road networks and a linear relationship between and urban population was found. The complexity of a road network is related not only to its geometric form, which can be described by , but also to its topological structure, which can be described by structural fractal dimension (). Whether some relations, such as allometric relations, exist between and other urban quantities is vague. This study explores the allometric relations between the of urban road networks and urban quantities in Hong Kong for the period from 1971 to 2011. It is found that has positive allometric relations with population, CO2 emissions, GDP, merchandise imports, and merchandise exports (with scaling exponents of 1.581, 4.298, 11.113, 13.951, and 14.141, respectively) but inverse allometric relations with the areas of arable and agricultural land (with scaling exponents of −2.857 and −1.918, respectively). These findings indicate that not only has allometric relations with urban quantities but also could have different types of relations. These discoveries could form another basis for the study of urban development.

[1]  Michael Batty,et al.  Fractal Cities: A Geometry of Form and Function , 1996 .

[2]  Yanguang Chen.  An allometric scaling relation based on logistic growth of cities , 2014 .

[3]  W. B. Marks,et al.  Fractal methods and results in cellular morphology — dimensions, lacunarity and multifractals , 1996, Journal of Neuroscience Methods.

[4]  Y Lee,et al.  An Allometric Analysis of the US Urban System: 1960 – 80 , 1989, Environment & planning A.

[5]  Peichao Gao,et al.  CRG Index: A More Sensitive Ht-Index for Enabling Dynamic Views of Geographic Features , 2016 .

[6]  M. Goodchild,et al.  The Fractal Nature of Geographic Phenomena , 1987 .

[7]  Christophe Claramunt,et al.  Topological Analysis of Urban Street Networks , 2004 .

[8]  Yanguang Chen,et al.  Characterizing Growth and Form of Fractal Cities with Allometric Scaling Exponents , 2010 .

[9]  Benoit B. Mandelbrot,et al.  Fractals in physics: Squig clusters, diffusions, fractal measures, and the unicity of fractal dimensionality , 1984 .

[10]  Shiguo Jiang,et al.  An analytical process of the spatio-temporal evolution of urban systems based on allometric and fractal ideas , 2009 .

[11]  B. Jiang,et al.  Ht-Index for Quantifying the Fractal or Scaling Structure of Geographic Features , 2013, 1305.0883.

[12]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[13]  Zhilin Li,et al.  Fractality and Self-Similarity in the Structure of Road Networks , 2012 .

[14]  C. Pantin.  Problems of Relative Growth , 1932, Nature.

[15]  Stig Nordbeck,et al.  URBAN ALLOMETRIC GROWTH , 1971 .

[16]  Yanguang Chen.  Urban chaos and replacement dynamics in nature and society , 2014 .

[17]  S. Havlin,et al.  How to calculate the fractal dimension of a complex network: the box covering algorithm , 2007, cond-mat/0701216.

[18]  L. V. Valen,et al.  A new evolutionary law , 1973 .

[19]  Dong Mu,et al.  Mixed Carbon Policies Based on Cooperation of Carbon Emission Reduction in Supply Chain , 2017 .

[20]  Hongrui Zhao,et al.  Unified Metrics for Characterizing the Fractal Nature of Geographic Features , 2017 .

[21]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[22]  M. Batty,et al.  Scaling and allometry in the building geometries of Greater London , 2008, 0804.2442.

[23]  S. Havlin,et al.  Self-similarity of complex networks , 2005, Nature.

[24]  D. Helbing,et al.  Growth, innovation, scaling, and the pace of life in cities , 2007, Proceedings of the National Academy of Sciences.

[25]  M. Guida,et al.  Topology of the Italian airport network: A scale-free small-world network with a fractal structure? , 2007 .

[26]  Yanguang Chen,et al.  Multi-Scaling Allometric Analysis for Urban and Regional Development: Model, Method, and Applications , 2011, 1105.5445.

[27]  Ulrik Brandes,et al.  What is network science? , 2013, Network Science.

[28]  Junmei Tang,et al.  Fractal Dimension of a Transportation Network and its Relationship with Urban Growth: A Study of the Dallas-Fort Worth Area , 2004 .

[29]  D'arcy W. Thompson,et al.  On Growth and Form , 1917, Nature.

[30]  M Batty,et al.  Preliminary Evidence for a Theory of the Fractal City , 1996, Environment & planning A.

[31]  Gang Liu,et al.  Characterizing Traffic Conditions from the Perspective of Spatial-Temporal Heterogeneity , 2016, ISPRS Int. J. Geo Inf..

[32]  Yanguang Chen,et al.  Modeling the self-affine structure and optimization conditions of city systems using the idea from fractals , 2009 .

[33]  Yanguang Chen.  Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis , 2010 .

[34]  M. Moses,et al.  Cities as Organisms: Allometric Scaling of Urban Road Networks , 2008 .

[35]  Yanguang Chen,et al.  A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991–2014 , 2016 .

[36]  Bruce E. Newling.  Urban Growth and Spatial Structure: Mathematical Models and Empirical Evidence , 1966 .

[37]  Frank Southworth,et al.  Fractal dimensions of metropolitan area road networks and the impacts on the urban built environment , 2016 .

[38]  C. Lo,et al.  CHINESE URBAN POPULATION ESTIMATES , 1977 .

[39]  L. Bettencourt,et al.  Urban scaling in Europe , 2015, Journal of The Royal Society Interface.