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Discrete Dynamics in Nature and Society
Volume 2010, Article ID 194715, 22 pages
http://dx.doi.org/10.1155/2010/194715
Research Article

Characterizing Growth and Form of Fractal Cities with Allometric Scaling Exponents

Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China

Received 9 August 2009; Revised 6 May 2010; Accepted 4 July 2010

Academic Editor: W. Ebeling

Copyright © 2010 Yanguang Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [34 citations]

The following is the list of published articles that have cited the current article.

  • Pan Liu, Xiao-Pu Han, and Linyuan Lu, “Triangle-mapping analysis on spatial competition and cooperation of Chinese cities,” IECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society, pp. 6012–6016, . View at Publisher · View at Google Scholar
  • Gavan S. McGrath, Anamika Shreevastava, and P. Suresh C. Rao, “Spatial analysis of the Surface Urban Heat Island,” Land Surface and Cryosphere Remote Sensing IV, pp. 11, . View at Publisher · View at Google Scholar
  • Yanguang Chen, “Derivation of the functional relations between fractal dimension of and shape indices of urban form,” Computers, Environment and Urban Systems, vol. 35, no. 6, pp. 442–451, 2011. View at Publisher · View at Google Scholar
  • Shougeng Hu, Qiuming Cheng, Le Wang, and Shuyun Xie, “Multifractal characterization of urban residential land price in space and time,” Applied Geography, vol. 34, pp. 161–170, 2012. View at Publisher · View at Google Scholar
  • Yanguang Chen, “The rank-size scaling law and entropy-maximizing principle,” Physica A: Statistical Mechanics and its Applications, vol. 391, no. 3, pp. 767–778, 2012. View at Publisher · View at Google Scholar
  • Yanguang Chen, “Zipf's law, 1/f noise, and fractal hierarchy,” Chaos Solitons & Fractals, vol. 45, no. 1, pp. 63–73, 2012. View at Publisher · View at Google Scholar
  • Yanguang Chen, “Zipf's Law, Hierarchical Structure, and Cards-Shuffling Model for Urban Development,” Discrete Dynamics in Nature and Society, vol. 2012, pp. 1–21, 2012. View at Publisher · View at Google Scholar
  • Yanguang Chen, “A set of formulae on fractal dimension relations and its application to urban form,” Chaos, Solitons & Fractals, vol. 54, pp. 150–158, 2013. View at Publisher · View at Google Scholar
  • Shougeng Hu, Qiuming Cheng, Le Wang, and Deyi Xu, “Modeling land price distribution using multifractal IDW interpolation and fractal filtering method,” Landscape and Urban Planning, vol. 110, pp. 25–35, 2013. View at Publisher · View at Google Scholar
  • Yanguang Chen, “An allometric scaling relation based on logistic growth of cities,” Chaos, Solitons & Fractals, vol. 65, pp. 65–77, 2014. View at Publisher · View at Google Scholar
  • K. Yakubo, Y. Saijo, and D. Korošak, “Superlinear and sublinear urban scaling in geographical networks modeling cities,” Physical Review E, vol. 90, no. 2, 2014. View at Publisher · View at Google Scholar
  • Yanguang Chen, “Urban chaos and replacement dynamics in nature and society,” Physica A: Statistical Mechanics and its Applications, 2014. View at Publisher · View at Google Scholar
  • Yanguang Chen, “The Spatial Meaning Of Pareto's Scaling Exponent Of City-Size Distributions,” Fractals-Complex Geometry Patterns and Scaling in Nature and Society, vol. 22, no. 1-2, 2014. View at Publisher · View at Google Scholar
  • Farideddin Peiravian, Amirhassan Kermanshah, and Sybil Derrible, “Spatial data analysis of complex urban systems,” Proceedings - 2014 IEEE International Conference on Big Data, IEEE Big Data 2014, pp. 1–6, 2014. View at Publisher · View at Google Scholar
  • Farideddin Peiravian, Amirhassan Kermanshah, and Sybil Derrible, “Spatial data analysis of complex urban systems,” Proceedings - 2014 IEEE International Conference on Big Data, IEEE Big Data 2014, pp. 54–59, 2014. View at Publisher · View at Google Scholar
  • Hongyu Luo, and Yanguang Chen, “An Allometric Algorithm for Fractal-Based Cobb-Douglas Function of Geographical Systems,” Discrete Dynamics in Nature and Society, vol. 2014, pp. 1–10, 2014. View at Publisher · View at Google Scholar
  • Yanguang Chen, “The distance-decay function of geographical gravity model: Power law or exponential law?,” Chaos Solitons & Fractals, vol. 77, pp. 174–189, 2015. View at Publisher · View at Google Scholar
  • Mauricio Santos-Vega, Pamela P. Martinez, and Mercedes Pascual, “Climate forcing and infectious disease transmission in urban landscapes: integrating demographic and socioeconomic heterogeneity,” Annals of the New York Academy of Sciences, 2016. View at Publisher · View at Google Scholar
  • Hadi Arbabi, and Martin Mayfield, “Urban and Rural—Population and Energy Consumption Dynamics in Local Authorities within England and Wales,” Buildings, vol. 6, no. 3, pp. 34, 2016. View at Publisher · View at Google Scholar
  • Yanguang Chen, “Multi-scaling allometric analysis for urban and regional development,” Physica A: Statistical Mechanics and its Applications, 2016. View at Publisher · View at Google Scholar
  • Mahbub Rashidpp. 1–453, 2016. View at Publisher · View at Google Scholar
  • Mahbub Rashid, and Mahbub Rashid, “Introduction,” The Geometry of Urban Layouts, pp. 3–11, 2016. View at Publisher · View at Google Scholar
  • Mahbub Rashid, and Mahbub Rashid, “Studies on the Geometry of Urban Layouts: A Review of the Literature,” The Geometry of Urban Layouts, pp. 19–45, 2016. View at Publisher · View at Google Scholar
  • Yanguang Chen, and Jiejing Wang, “Describing Urban Evolution with the Fractal Parameters Based on Area-Perimeter Allometry,” Discrete Dynamics in Nature and Society, vol. 2016, pp. 1–14, 2016. View at Publisher · View at Google Scholar
  • Nicholas Z. Muller, and Akshaya Jha, “Does environmental policy affect scaling laws between population and pollution? Evidence from American metropolitan areas,” Plos One, vol. 12, no. 8, pp. e0181407, 2017. View at Publisher · View at Google Scholar
  • Camilo Rodrigues Neto, Fabiano L. Ribeiro, Joao Meirelles, and Fernando F. Ferreira, “A model of urban scaling laws based on distance dependent interactions,” Royal Society Open Science, vol. 4, no. 3, pp. 160926, 2017. View at Publisher · View at Google Scholar
  • Lei Dong, Hao Wang, and Hongrui Zhao, “The definition of city boundary and scaling law,” Dili Xuebao/Acta Geographica Sinica, vol. 72, no. 2, pp. 213–223, 2017. View at Publisher · View at Google Scholar
  • Fang Zeng, Xiang Li, and Ke Li, “Modeling complexity in engineered infrastructure system: Water distribution network as an example,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 27, no. 2, pp. 023105, 2017. View at Publisher · View at Google Scholar
  • Karen C Seto, Michail Fragkias, and José Lobo, “A comparison of nighttime lights data for urban energy research: Insights from scaling analysis in the US system of cities,” Environment and Planning B: Urban Analytics and City Science, vol. 44, no. 6, pp. 1077–1096, 2017. View at Publisher · View at Google Scholar
  • Pradeep Adhikari, and Kirsten M. de Beurs, “Growth in urban extent and allometric analysis of West African cities,” Journal of Land Use Science, pp. 1–20, 2017. View at Publisher · View at Google Scholar
  • Yanguang Chen, and Jian Feng, “A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991–2014,” Discrete Dynamics in Nature and Society, vol. 2017, pp. 1–15, 2017. View at Publisher · View at Google Scholar
  • Yanguang Chen, and Bin Jiang, “Hierarchical Scaling in Systems of Natural Cities,” Entropy, vol. 20, no. 6, pp. 432, 2018. View at Publisher · View at Google Scholar
  • Yu Fang, and James W. Jawitz, “Data Descriptor: High-resolution reconstruction of the United States human population distribution, 1790 to 2010,” Scientific Data, vol. 5, 2018. View at Publisher · View at Google Scholar
  • Wenjia Wu, Hongrui Zhao, Qifan Tan, and Peichao Gao, “An Urban Scaling Estimation Method in a Heterogeneity Variance Perspective,” Entropy, vol. 21, no. 4, pp. 337, 2019. View at Publisher · View at Google Scholar