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Fractal analytical approach of urban form based on spatial correlation function

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  • Chen, Yanguang

Abstract

Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities are not yet revealed in theory. By mathematical deduction and transform (e.g., Fourier transform), I find that scaling analysis, spectral analysis, and spatial correlation analysis are all associated with fractal concepts and can be integrated into a new approach to fractal analysis of cities. This method can be termed ‘3S analyses’ of urban form. Using the 3S analysis, I derived a set of fractal parameter equations, by which different fractal parameters of cities can be linked up with one another. Each fractal parameter has its own reasonable extent of values. According to the fractal parameter equations, the intersection of the rational ranges of different fractal parameters suggests the proper scale of the fractal dimension of urban patterns, which varies from 1.5 to 2. The fractal dimension equations based on the 3S analysis and the numerical relationships between different fractal parameters are useful for geographers to understand urban evolution and potentially helpful for future city planning.

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  • Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
    • Handle: RePEc:eee:chsofr:v:49:y:2013:i:c:p:47-60
    DOI: 10.1016/j.chaos.2013.02.006
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    References listed on IDEAS

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    Cited by:

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    2. Estelle Mennicken & Rémi Lemoy & Geoffrey Caruso, 2024. "Road network distances and detours in Europe: Radial profiles and city size effects," Environment and Planning B, , vol. 51(1), pages 174-194, January.
    3. Yanguang Chen, 2015. "A New Methodology of Spatial Cross-Correlation Analysis," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-20, May.
    4. DELLOYE, Justin & LEMOY, Rémi & CARUSO, Geoffrey, 2017. "Alonso and the scaling of urban profiles," LIDAM Discussion Papers CORE 2017037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Yanguang Chen, 2021. "An analytical process of spatial autocorrelation functions based on Moran’s index," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-27, April.
    6. Li, Huanhuan & Xu, Beibei & Riasi, Alireza & Szulc, Przemyslaw & Chen, Diyi & M'zoughi, Fares & Skjelbred, Hans Ivar & Kong, Jiehong & Tazraei, Pedram, 2019. "Performance evaluation in enabling safety for a hydropower generation system," Renewable Energy, Elsevier, vol. 143(C), pages 1628-1642.
    7. 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.
    8. Fatemeh Jahanmiri & Dawn Cassandra Parker, 2022. "An Overview of Fractal Geometry Applied to Urban Planning," Land, MDPI, vol. 11(4), pages 1-23, March.
    9. Chen, Yanguang, 2017. "Multi-scaling allometric analysis for urban and regional development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 673-689.
    10. Lang, Wei & Long, Ying & Chen, Tingting & Li, Xun, 2019. "Reinvestigating China’s urbanization through the lens of allometric scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1429-1439.
    11. Xu, Beibei & Chen, Diyi & Zhang, Hao & Wang, Feifei, 2015. "Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 50-61.
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    13. 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.

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