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An analytical process of the spatio-temporal evolution of urban systems based on allometric and fractal ideas

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  • Chen, Yanguang
  • Jiang, Shiguo

Abstract

This paper presents a computer-based analytical framework for the spatio-temporal evolution of urban systems using the ideas from the allometric growth associated with fractals. Both cities as systems and systems of cities follow the law of allometric growth, and the scaling factors of the allometric relations can compose the matrix equations as eigenfunctions. The fractal dimension arrays are just the eigenvectors of the scaling factor matrices while the numbers of variables are the greatest eigenvalues. The solutions of matrix equations can be employed to analyse city systems and evaluate relative levels of urban development. The method is applied to Hangzhou urban system of China. The results reveal clearly an urbanization process characterized as population concentration and an industrialization process characterized as industrial diffusion. The computation results are consistent with the reality, which indicate that the method is available for analyzing the spatio-temporal evolution of complex systems such as cities.

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  • Chen, Yanguang & Jiang, Shiguo, 2009. "An analytical process of the spatio-temporal evolution of urban systems based on allometric and fractal ideas," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 49-64.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:1:p:49-64
    DOI: 10.1016/j.chaos.2007.01.130
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    2. Man, Wang & Nie, Qin & Li, Zongmei & Li, Hui & Wu, Xuewen, 2019. "Using fractals and multifractals to characterize the spatiotemporal pattern of impervious surfaces in a coastal city: Xiamen, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 44-53.
    3. Wang, Ping & Gu, Changgui & Yang, Huijie & Wang, Haiying, 2022. "The multi-scale structural complexity of urban morphology in China," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Chen, Yanguang, 2014. "Urban chaos and replacement dynamics in nature and society," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 373-384.
    5. Chen, Yanguang & Feng, Jian, 2012. "Fractal-based exponential distribution of urban density and self-affine fractal forms of cities," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1404-1416.
    6. 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.
    7. Chumki Shikary & Somnath Rudra, 2024. "Assessment of urban-to-urban interaction and its impact on urban development: a study on a backward district of Eastern India," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 26(7), pages 16863-16886, July.
    8. 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.
    9. Zhijun SONG & Linjun YU, 2019. "Multifractal features of spatial variation in construction land in Beijing (1985–2015)," Palgrave Communications, Palgrave Macmillan, vol. 5(1), pages 1-15, December.
    10. Chen, Yanguang & Feng, Jian, 2017. "Spatial analysis of cities using Renyi entropy and fractal parameters," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 279-287.
    11. 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.
    12. 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.
    13. Jian Feng & Yanguang Chen, 2010. "Spatiotemporal Evolution of Urban Form and Land-Use Structure in Hangzhou, China: Evidence from Fractals," Environment and Planning B, , vol. 37(5), pages 838-856, October.
    14. Chen, Yanguang, 2015. "The distance-decay function of geographical gravity model: Power law or exponential law?," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 174-189.
    15. Zhijun Song & Linjun Yu, 2015. "A study on the generalised space of urban–rural integration in Beijing suburbs during the present day," Urban Studies, Urban Studies Journal Limited, vol. 52(14), pages 2581-2598, November.
    16. Song, Zhijun & Jin, Wenxuan & Jiang, Guanghui & Li, Sichun & Ma, Wenqiu, 2021. "Typical and atypical multifractal systems of urban spaces—using construction land in Zhengzhou from 1988 to 2015 as an example," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

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