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Ht-Index for Quantifying the Fractal or Scaling Structure of Geographic Features

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  • Bin Jiang
  • Junjun Yin

Abstract

Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is dubious, is mainly attributed to the strict definition of fractal dimension as a measure or index for characterizing the complexity of fractals. In this article, we propose an alternative, ht-index, to quantify the fractal or scaling structure of geographic features. A geographic feature has ht-index (h) if the pattern of far more small things than large ones recurs (h – 1) times at different scales. The higher the ht-index, the more complex the geographic feature. We conduct three case studies to illustrate how the computed ht-indexes capture the complexity of different geographic features. We further discuss how ht-index is complementary to fractal dimension and elaborate on a dynamic view behind ht-index that enables better understanding of geographic forms and processes.

Suggested Citation

  • Bin Jiang & Junjun Yin, 2014. "Ht-Index for Quantifying the Fractal or Scaling Structure of Geographic Features," Annals of the American Association of Geographers, Taylor & Francis Journals, vol. 104(3), pages 530-540, May.
    • Handle: RePEc:taf:raagxx:v:104:y:2014:i:3:p:530-540
    DOI: 10.1080/00045608.2013.834239
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    Cited by:

    1. Michael J Dawes & Michael J Ostwald, 2020. "The mathematical structure of Alexander’s A Pattern Language: An analysis of the role of invariant patterns," Environment and Planning B, , vol. 47(1), pages 7-24, January.
    2. Francisco Martínez & Bastian Sepúlveda & Hermann Manríquez, 2023. "Fractal Organization of Chilean Cities: Observations from a Developing Country," Land, MDPI, vol. 12(2), pages 1-21, January.
    3. Boeing, Geoff, 2018. "Measuring the Complexity of Urban Form and Design," SocArXiv bxhrz, Center for Open Science.
    4. Bin Jiang, 2019. "A Recursive Definition of Goodness of Space for Bridging the Concepts of Space and Place for Sustainability," Sustainability, MDPI, vol. 11(15), pages 1-13, July.
    5. Xiaoyang Han & Sijing Ye & Shuyi Ren & Changqing Song, 2023. "Using the DTFM Method to Analyse the Degradation Process of Bilateral Trade Relations between China and Australia," Sustainability, MDPI, vol. 15(9), pages 1-22, April.
    6. Wei Zhu & Ding Ma & Zhigang Zhao & Renzhong Guo, 2020. "Investigating the Complexity of Spatial Interactions between Different Administrative Units in China Using Flickr Data," Sustainability, MDPI, vol. 12(22), pages 1-12, November.
    7. Jiang, Bin & Ma, Ding, 2015. "Defining least community as a homogeneous group in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 154-160.
    8. António Dinis F. Santos & Duarte Valério & J. A. Tenreiro Machado & António M. Lopes, 2019. "A fractional perspective to the modelling of Lisbon’s public transportation network," Transportation, Springer, vol. 46(5), pages 1893-1913, October.
    9. Nimrod Serok & Orr Levy & Shlomo Havlin & Efrat Blumenfeld-Lieberthal, 2019. "Unveiling the inter-relations between the urban streets network and its dynamic traffic flows: Planning implication," Environment and Planning B, , vol. 46(7), pages 1362-1376, September.
    10. Ding Ma & Itzhak Omer & Toshihiro Osaragi & Mats Sandberg & Bin Jiang, 2019. "Why topology matters in predicting human activities," Environment and Planning B, , vol. 46(7), pages 1297-1313, September.
    11. Taylor M. Oshan & Levi J. Wolf & Mehak Sachdeva & Sarah Bardin & A. Stewart Fotheringham, 2022. "A scoping review on the multiplicity of scale in spatial analysis," Journal of Geographical Systems, Springer, vol. 24(3), pages 293-324, July.
    12. Chen, Yanguang & Wang, Yihan & Li, Xijing, 2019. "Fractal dimensions derived from spatial allometric scaling of urban form," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 122-134.
    13. Tsiotas, Dimitrios, 2021. "Drawing indicators of economic performance from network topology: The case of the interregional road transportation in Greece," Research in Transportation Economics, Elsevier, vol. 90(C).
    14. Bin Jiang, 2019. "Natural Cities Generated from All Building Locations in America," Data, MDPI, vol. 4(2), pages 1-5, April.

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