IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v194y2025ics0960077925001262.html
   My bibliography  Save this article

A segmented fractal model associated with the spatial distribution characteristics of urban rail transit network

Author

Listed:
  • Chen, Ding
  • Mei, Mengjun
  • Jiang, Jin
  • Wang, Cheng

Abstract

In view of the limitations of fractal models with single fractal dimension in representing the spatial non-uniform distribution of urban rail transit network, a segmented fractal model is established by summarizing the variation patterns of inflection points in network length curves and the definition of binary classification in spatial distribution analysis. This model adheres to the countable additivity definition of the measurement for disjoint fractal sets and retains the inherent measurement relationship in fractal theory. By examining the results of spatial distribution analysis derived from typical urban rail transit network data, the correlation between model parameters and spatial distribution characteristics is investigated. This process validates the effectiveness of the model while also exploring the physical meaning of its parameters. The results show that the segmented point in this model divides the network into two domains. The fractal dimensions corresponding to the first and second domains are relatively independent and can be utilized to characterize the spatial heterogeneous growth rate of the network. Segmented point in this model is identified as the main parameter that exhibits significant positive correlations with the spatial distribution characteristics, including the standard deviation distance, semi-major axis and semi-minor axis. The correlation coefficients are 0.89, 0.90, and 0.75, respectively. These results indicate that the network located within the first domain demonstrates an aggregation distribution characteristic, whereas that within the second domain exhibits a dispersion distribution characteristic. Besides, the parameters in the model have been found to inadequately reflect the intensity of directional distribution within the network. However, the segmented point within these model parameters can serve as an indicator for the coverage range of a directionally distributed network along both its semi-major and semi-minor axes.

Suggested Citation

  • Chen, Ding & Mei, Mengjun & Jiang, Jin & Wang, Cheng, 2025. "A segmented fractal model associated with the spatial distribution characteristics of urban rail transit network," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001262
    DOI: 10.1016/j.chaos.2025.116113
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925001262
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116113?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Chen, Yanguang, 2013. "A set of formulae on fractal dimension relations and its application to urban form," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 150-158.
    2. Roberto Bachi, 1962. "Standard Distance Measures And Related Methods For Spatial Analysis," Papers in Regional Science, Wiley Blackwell, vol. 10(1), pages 83-132, January.
    3. Yuqing Long & Yanguang Chen, 2021. "Multifractal scaling analyses of urban street network structure: The cases of twelve megacities in China," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-23, February.
    4. Yanguang Chen, 2010. "Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-20, December.
    5. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    6. Xuanxuan Xia & Hongchang Li & Xujuan Kuang & Jack Strauss, 2021. "Spatial–Temporal Features of Coordination Relationship between Regional Urbanization and Rail Transit—A Case Study of Beijing," IJERPH, MDPI, vol. 19(1), pages 1-30, December.
    7. Jiao Li & Yongsheng Qian & Junwei Zeng & Fan Yin & Leipeng Zhu & Xiaoping Guang, 2020. "Research on the Influence of a High-Speed Railway on the Spatial Structure of the Western Urban Agglomeration Based on Fractal Theory—Taking the Chengdu–Chongqing Urban Agglomeration as an Example," Sustainability, MDPI, vol. 12(18), pages 1-13, September.
    8. Shushan Chai & Qinghuai Liang & Simin Zhong, 2019. "Design of Urban Rail Transit Network Constrained by Urban Road Network, Trips and Land-Use Characteristics," Sustainability, MDPI, vol. 11(21), pages 1-23, November.
    9. Moreno-Pulido, Soledad & Pavón-Domínguez, Pablo & Burgos-Pintos, Pedro, 2021. "Temporal evolution of multifractality in the Madrid Metro subway network," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rasul Kochkarov & Azret Kochkarov, 2022. "Introduction to the Class of Prefractal Graphs," Mathematics, MDPI, vol. 10(14), pages 1-17, July.
    2. Pooler, James A., 1995. "The use of spatial separation in the measurement of transportation accessibility," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(6), pages 421-427, November.
    3. Yao, Jialing & Sun, Bingbin & Xi, lifeng, 2019. "Fractality of evolving self-similar networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 211-216.
    4. Duan, Shuyu & Wen, Tao & Jiang, Wen, 2019. "A new information dimension of complex network based on Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 529-542.
    5. Ikeda, Nobutoshi, 2020. "Fractal networks induced by movements of random walkers on a tree graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    6. Sun, Bingbin & Yao, Jialing & Xi, Lifeng, 2019. "Eigentime identities of fractal sailboat networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 338-349.
    7. Ma, Fei & Ouyang, Jinzhi & Shi, Haobin & Pan, Wei & Wang, Ping, 2024. "Type-II Apollonian network: More robust and more efficient Apollonian network," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    8. Lu, Qing-Chang & Xu, Peng-Cheng & Zhao, Xiangmo & Zhang, Lei & Li, Xiaoling & Cui, Xin, 2022. "Measuring network interdependency between dependent networks: A supply-demand-based approach," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    9. Lambiotte, R. & Panzarasa, P., 2009. "Communities, knowledge creation, and information diffusion," Journal of Informetrics, Elsevier, vol. 3(3), pages 180-190.
    10. Zhang, Qi & Luo, Chuanhai & Li, Meizhu & Deng, Yong & Mahadevan, Sankaran, 2015. "Tsallis information dimension of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 707-717.
    11. Aldrich, Preston R. & El-Zabet, Jermeen & Hassan, Seerat & Briguglio, Joseph & Aliaj, Enela & Radcliffe, Maria & Mirza, Taha & Comar, Timothy & Nadolski, Jeremy & Huebner, Cynthia D., 2015. "Monte Carlo tests of small-world architecture for coarse-grained networks of the United States railroad and highway transportation systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 32-39.
    12. Retière, N. & Sidqi, Y. & Frankhauser, P., 2022. "A steady-state analysis of distribution networks by diffusion-limited-aggregation and multifractal geometry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    13. Xiaojian Yu & Zhiqing Zhao, 2021. "Fractal Characteristic Evolution of Coastal Settlement Land Use: A Case of Xiamen, China," Land, MDPI, vol. 11(1), pages 1-12, December.
    14. Xi, Lifeng & Wang, Lihong & Wang, Songjing & Yu, Zhouyu & Wang, Qin, 2017. "Fractality and scale-free effect of a class of self-similar networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 31-40.
    15. Meng, Xiangyi & Zhou, Bin, 2023. "Scale-free networks beyond power-law degree distribution," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    16. Yin, Likang & Deng, Yong, 2018. "Measuring transferring similarity via local information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 102-115.
    17. Fan Xu & Zeng Zhou & Sergio Fagherazzi & Andrea D’Alpaos & Ian Townend & Kun Zhao & Weiming Xie & Leicheng Guo & Xianye Wang & Zhong Peng & Zhicheng Yang & Chunpeng Chen & Guangcheng Cheng & Yuan Xu &, 2024. "Anomalous scaling of branching tidal networks in global coastal wetlands and mudflats," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    18. Haosu Zhao & Bart Julien Dewancker & Feng Hua & Junping He & Weijun Gao, 2020. "Restrictions of Historical Tissues on Urban Growth, Self-Sustaining Agglomeration in Walled Cities of Chinese Origin," Sustainability, MDPI, vol. 12(14), pages 1-29, July.
    19. Rosenberg, Eric, 2018. "Generalized Hausdorff dimensions of a complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 1-17.
    20. Xuezai Pan & Xudong Shang, 2022. "The Uniform Convergence Property of Sequence of Fractal Interpolation Functions in Complicated Networks," Mathematics, MDPI, vol. 10(20), pages 1-8, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001262. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.