• Journal of Geo-information Science
  • Vol. 22, Issue 4, 827 (2020)
Hong ZHANG1、1、2、2、*, Tian LAN3、3, and Zhilin LI2、2、3、3
Author Affiliations
  • 1School of Urban and Regional Science, East China Normal Unviersity, Shanghai 200062, China
  • 1华东师范大学城市与区域科学学院,上海 200062
  • 2Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China
  • 2西南交通大学地球科学与环境工程学院,成都 611756
  • 3Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong 999077, China
  • 3香港理工大学土地测量与地理资讯系,香港 999077
  • show less
    DOI: 10.12082/dqxxkx.2020.200160 Cite this Article
    Hong ZHANG, Tian LAN, Zhilin LI. Advances in Fractal Cities: A Shift from Morphology to Network[J]. Journal of Geo-information Science, 2020, 22(4): 827 Copy Citation Text show less
    References

    [1] [M]. Triumph of the city: How our greatest invention makes us richer, smarter, greener, healthier, and happier(2011).

    [2] [M]. The social logic of space(1984).

    [3] The informational city: information technology, economic restructuring, and the urban-regional process[M]. New York: Wiley-Blackwell(1989).

    [4] [M]. Space is the machine: A configurational theory of architecture(1996).

    [5] [M]. Determinants of the growth and decline of cities in north America. In: Kresl P, Gapper G. (eds) North American cities and the global economy: challenges and opportunities(1995).

    [6] et alAllometric scaling, size distribution, and pattern formation of natural cities[J]. Palgrave Communications, 1, 15017(2015).

    [7] Cerdá: the five bases of the general theory of urbanization[M]. Barcelona, Spain: Electa(1999).

    [8] Civics: As applied sociology[M]. Boston, MA: Qontro Classic Books(2010).

    [9] 潘峰华, 方成, 李仙德. 中国城市网络研究评述与展望[J]. 地理科学, 2019,39(7):1093-1101. [ PanF H, FangC, LiX D. The progress and prospect of research on Chinese city network[J]. Scientia Geographica Sinica, 2019,39(7):1093-1101. ] [ Pan F H, Fang C, Li X D. The progress and prospect of research on Chinese city network[J]. Scientia Geographica Sinica, 2019,39(7):1093-1101. ]

    [10] [M]. The new science of cities(2013).

    [11] [M]. Scale: the universal laws of growth, innovation, sustainability, and the pace of life in organisms, cities, economies, and companies(2017).

    [12] The origins of scaling in cities[J]. Science, 340, 1438-1441(2013).

    [13] [M]. Fractal cities: A geometry of form and function(1994).

    [14] 刘继生, 陈彦光. 城市地理分形研究的回顾与前瞻[J]. 地理科学, 2000,20(2):166-171. [ LiuJ S, ChenY G. Fractal studies of urban geography in the past and future[J]. Scientia Geographica Sinica, 2000,20(2):166-171. ] [ Liu J S, Chen Y G. Fractal studies of urban geography in the past and future[J]. Scientia Geographica Sinica, 2000,20(2):166-171. ]

    [15] 秦耀辰, 刘凯. 分形理论在地理学中的应用研究进展[J]. 地理科学进展, 2003,22(4):426-436. [ QinY C, LiuK. Research progress of fractal theory in geography[J]. Progress in Geography, 2003,22(4):426-436.] [ Qin Y C, Liu K. Research progress of fractal theory in geography[J]. Progress in Geography, 2003,22(4):426-436.]

    [16] [M]. Cities and complexity: understanding cities with cellular automata, agent-based models, and fractals(2007).

    [17] 陈彦光. 分形城市系统:标度·对称·空间复杂性[M]. 北京: 科学出版社, 2008. [ ChenY G. Fractal urban systems: Scaling, symmetry, and spatial complexity[M]. Beijing: Science Press, 2008. ] [ Chen Y G. Fractal urban systems: Scaling, symmetry, and spatial complexity[M]. Beijing:Science Press, 2008. ]

    [18] Fractality and self-similarity in the structure of road networks[J]. Annals of the Association of American Geographers, 102, 350-365(2012).

    [19] How long is the coast of Britain? statistical self-similarity and fractional dimension[J]. Science, 156, 636-638(1967).

    [20] The fractal geometry of nature[M]. New York: W.H. Freeman(1982).

    [21] 陈彦光, 陈文惠. GIS与地理现象的分形研究[J]. 东北师大学报(自然科学版), 1998(2):91-96. [ ChenY G, ChenW H. GIS and fractal studies of geographical phenomena[J]. Journal of Northeast Normal University, 1998(2):91-96. ] [ Chen Y G, Chen W H. GIS and fractal studies of geographical phenomena[J]. Journal of Northeast Normal University, 1998(2):91-96. ]

    [22] The fourth dimension of life: fractal geometry and allometric scaling of organisms[J]. Science, 284, 1677-1679(1999).

    [23] Self-organization and the city[M]. Berlin:Springer-Verlag(2000).

    [24] Fractals take a central place[J]. Geografiska Annaler: Series B, Human Geography, 67, 83-88(1985).

    [25] The fractal nature of geographic phenomena[J]. Annals of the Association of American Geographers, 77, 265-278(1987).

    [26] 李后强, 艾南山. 具有黄金分割特征和分形性质的市场网络[J]. 经济地理, 1992,12(4):1-5. [ LiH Q, AiN S. With gold segmentation features and fractal properties of the market network[J]. Economic Geography, 1992,12(4):1-5. ] [ Li H Q, Ai N S. With gold segmentation features and fractal properties of the market network[J]. Economic Geography, 1992,12(4):1-5. ]

    [27] 刘继生, 陈彦光. 城镇体系空间结构的分形维数及其测算方法[J]. 地理研究, 1999,18(2):171-178. [ LiuJ S, ChenY G. Fractal dimension of spatial structure of an urban system and the methods of their determination[J]. Geographical Research, 1999,18(2):171-178. ] [ Liu J S, Chen Y G. Fractal dimension of spatial structure of an urban system and the methods of their determination[J]. Geographical Research, 1999,18(2):171-178. ]

    [28] 蔡金华, 龙毅, 毋河海, 等. 基于反S数学模型的地图目标分形无标度区自动确定[J]. 武汉大学学报·信息科学版, 2004,29(3):249-253. [ CaiJ H, LongY, WuH H, et al. Automatic determination of fractal non-scale interval of map objects based on inverse 'S' mathematical model[J]. Geomatics and Information Science of Wuhan University, 2004,29(3):249-253. ] [ Cai J H, Long Y, Wu H H, et al. Automatic determination of fractal non-scale interval of map objects based on inverse 'S' mathematical model[J]. Geomatics and Information Science of Wuhan University, 2004,29(3):249-253. ]

    [29] 陈彦光, 刘继生. 城市形态分维测算和分析的若干问题[J]. 人文地理, 2007,22(3):104-109. [ ChenY G, LiuJ S. On fractal dimension calculation and analysis of urban form[J]. Human Geography, 2007,22(3):104-109. ] [ Chen Y G, Liu J S. On fractal dimension calculation and analysis of urban form[J].Human Geography, 2007,22(3):104-109. ]

    [30] Spatial complexity of the urban-rural road network. Wuhan: Central China Normal University(2011).

    [31] Self-similarity of complex networks[J]. Nature, 433, 392(2005).

    [32] 王江涛, 杨建梅. 复杂网络的分形研究方法综述[J]. 复杂系统与复杂性科学, 2013,10(4):1-7. [ WangJ T, YangJ M. The review on fractal research of complex network[J]. Complex Systems and Complexity Science, 2013,10(4):1-7. ] [ Wang J T, Yang J M. The review on fractal research of complex network[J]. Complex Systems and Complexity Science, 2013,10(4):1-7. ]

    [33] et alFractal dimensions of metropolitan area road networks and the impacts on the urban built environment[J]. Ecological indicators, 70, 285-296(2016).

    [34] Fractal texture and structure of central place system[J]. Fractals, 28, 2050008(2017).

    [35] Urban allometric scaling beneath structural fractality of road networks[J]. Annals of the American Association of Geographers, 109, 943-957(2019).

    [36] et alGrowth, innovation, scaling, and the pace of life in cities[J]. Proceedings of the National Academy of Sciences of the United States of America, 104, 7301(2007).

    [37] 陈彦光. 城市异速标度研究的起源,困境和复兴[J]. 地理研究, 2013,32(6):1033-1045. [ ChenY G. The rise, fall, and revival process of allometric scaling analysis in urban studies[J]. Geographical Research, 2013,32(6):1033-1045. ] [ Chen Y G. The rise, fall, and revival process of allometric scaling analysis in urban studies[J]. Geographical Research, 2013,32(6):1033-1045. ]

    [38] Multi-scaling allometric analysis for urban and regional development[J]. Physica A: Statistical Mechanics and its Applications, 465, 673-689(2017).

    [39] The mysteries of mass[J]. Scientifific American, 293, 40-48(2005).

    [40] [M]. Digital terrain modeling:principles and methodology(2004).

    [41] 朱晓华. 地理空间信息的分形与分维[M]. 北京: 测绘出版社, 2007. [ ZhuX H. Fractal and fractal dimensions of spatial geo-information[M]. Beijing: Surveying and Mapping Press, 2007. ] [ Zhu X H. Fractal and fractal dimensions of spatial geo-information[M]. Beijing: Surveying and Mapping Press, 2007. ]

    [42] Deux types fondamentaux de distribution statistique[J]. Bull, de L'Institut International de Statistique, 111, 295-299(1938).

    [43] The problem of contiguity;an appendix to statistics of deadly quarrels[J]. General Systems Yearbook, 6, 139-187(1961).

    [44] [M]. Fractals(2013).

    [45] [M]. Algorithmic foundation of multi-scale spatial representation(2006).

    [46] et alWhen and where is a city fractal?[J]. Environment and Planning B: Planning and Design, 27, 507-519(2000).

    [47] 陈彦光. 城市形态的分维估算与分形判定[J]. 地理科学进展, 2017,36(5); 529-539. [ ChenY G. Approaches to estimating fractal dimension and identifying fractals of urban form[J]. Progress in Geography, 2017,36(5):529-539. ] [ Chen Y G. Approaches to estimating fractal dimension and identifying fractals of urban form[J]. Progress in Geography, 2017,36(5):529-539. ]

    [48] Topological analysis of urban street networks[J]. Environment and Planning B: Planning and Design, 31, 151-162(2004).

    [49] et alWhy topology matters in predicting human activities[J]. Environment and Planning B: Urban Analytics and City Science, 46, 12971-1313(2019).

    [50] Cities and nature(2nd ed)[M]. London and New York: Routledge(2013).

    [51] Complexity as a link between space and place[J]. Environment and Planning A: Economy and Space, 38, 647-664(2006).

    [52] Self-organizing cities[J]. Futures, 29, 131-138(1997).

    [53] et al分形理论在人文地理学中的应用研究[J]. 地理学与国土研究, 17, 51-56(2001).

    [54] 刘继生, 陈彦光. 城市,分形与空间复杂性探索[J]. 复杂系统与复杂性科学, 2004,1(3):62-69. [ LiuJ S, ChenY G. Exploration of city, fractal and space complexity[J]. Complex Systems and Complexity Science, 2004,1(3):62-69. ] [ Liu J S, Chen Y G. Exploration of city, fractal and space complexity[J]. Complex Systems and Complexity Science, 2004,1(3):62-69. ]

    [55] 刘继生, 陈彦光. 作为CAS的复杂城市地理系统的SOC性质[J]. 地理科学, 2007,27(2):129-135. [ LiuJ S, ChenY G. SOC properties of complex urban geographic system as CAS[J]. Scientia Geographica Sinica, 2007,27(2):129-135. ] [ Liu J S, Chen Y G. SOC properties of complex urban geographic system as CAS[J]. Scientia Geographica Sinica, 2007,27(2):129-135. ]

    [56] 陈彦光. 分形城市与城市规划[J]. 城市规划, 2005(2):33-40,51. [ ChenY G. Fractal cities and city planning[J]. China City Planning Review, 2005(2):33-40,51. ] [ Chen Y G. Fractal cities and city planning[J]. China City Planning Review, 2005(2):33-40,51. ]

    [57] 陈彦光. 简单,复杂与地理分布模型的选择[J]. 地理科学进展, 2015,34(3):321-329. [ ChenY G. Simple, complex and the selection of geographical distribution model[J]. Progress in Geography, 2015,34(3):321-329. ] [ Chen Y G. Simple, complex and the selection of geographical distribution model[J]. Progress in Geography, 2015,34(3):321-329. ]

    [58] 刘承良, 余瑞林, 段德忠. 武汉城市圈城乡道路网分形的时空结构[J]. 地理研究, 2014,33(4):777-788. [ LiuC L, YuR L, DuanD Z. Spatio-temporal structure of urban and rural road network fractal in Wuhan urban circle[J]. Geographical Research, 2014,33(4):777-788.] [ Liu C L, Yu R L, Duan D Z. Spatio-temporal structure of urban and rural road network fractal in Wuhan urban circle[J]. Geographical Research, 2014,33(4):777-788.]

    [59] 刘承良, 殷美元, 黄丽. 基于多中心性分析的中国交通网络互补性的空间格局[J]. 经济地理, 2018,38(10):21-28. [ LiuC L, YinM Y, HuangL. The spatial pattern of complementarity of china's transportation network based on multi-centricity analysis[J]. Economic Geography, 2018,38(10):21-28. ] [ Liu C L, Yin M Y, Huang L. The spatial pattern of complementarity of china's transportation network based on multi-centricity analysis[J]. Economic Geography, 2018,38(10):21-28. ]

    [60] The fractal simulation of urban structure[J]. Environment and Planning A:Economy and Space, 18, 1143-1179(1986).

    [61] Urban shapes as fractals[J]. Area, 19, 215-221(1987).

    [62] The morphology of urban landuse[J]. Environment and Planning B: Planning and Design, 15, 461-488(1988).

    [63] Urban growth and form: scaling, fractal geometry, and diffusion-limited aggregation[J]. Environment and Planning A: Economy and Space, 2, 1447-1472(1989).

    [64] Fractal-based description of urban form[J]. Environment and Planning B: Planning and Design, 14, 123-134(1987).

    [65] Fractals: New ways of looking at cities[J]. Nature, 377, 574(1995).

    [66] 冒卓影, 冒亚龙, 何镜堂. 国外分形建筑研究与展望[J]. 建筑师, 2016,2(4):13-20. [ MaoZ Y, MaoY L, HeJ T. Research and prospect of fractal architecture abroad[J]. The Architect, 2016,2(4):13-20. ] [ Mao Z Y, Mao Y L, He J T. Research and prospect of fractal architecture abroad[J]. The Architect, 2016,2(4):13-20. ]

    [67] Fractal geometry in architecture and design[M]. Boston: Birkhauser(1996).

    [68] Fractal dimension and fractal growth of urbanized areas[J]. International Journal of Geographical Information Science, 16, 419-437(2002).

    [69] 赵晶, 徐建华, 梅安新, 等. 上海市土地利用结构和形态演变的信息熵与分维分析[J]. 地理研究, 2004,23(2):137-146. [ ZhaoJ, XuJ H, MeiX A, et al. Information entropy and fractal dimension analysis of the evolution of land use structure and form in Shanghai[J]. Geographical Research, 2004,23(2):137-146. ] [ Zhao J, Xu J H, Mei X A, et al. Information entropy and fractal dimension analysis of the evolution of land use structure and form in Shanghai[J]. Geographical Research, 2004,23(2):137-146. ]

    [70] 刘承良, 段德忠. 武汉城市圈道路网空间生长的分形研究. 交通运输系统工程与信息, 2013,13(5); 185-193. [ LiuC L, DuanD Z. Fractal study on spatial growth of road network in Wuhan urban circle[J]. Journal of Transportation Systems Engineering and Information Technology, 2013,13(5):185-193. ] [ Liu C L, Duan D Z. Fractal study on spatial growth of road network in Wuhan urban circle[J]. Journal of Transportation Systems Engineering and Information Technology, 2013,13(5):185-193. ]

    [71] Rank clocks[J]. Nature, 444, 592-596(2006).

    [72] [M]. Inventing future cities(2018).

    [73] Rivers and central places: analogous systems?[J]. Journal of Regional Science, 129-139(1967).

    [74] Relationships between fractal road and drainage networks in Wuling mountainous area: another symmetric understanding of human-environment relations[J]. Journal of Mountain Science, 11, 1060-1069(2014).

    [75] Fractal dimensions of the built-up footprint: Buildings versus roads. fractal evidence from Antwerp (Belgium)[J]. Environment and Planning B: Planning and Design, 40, 310-329(2013).

    [76] et alCity population dynamics and fractal transport networks[J]. Proceedings of the Santa Fe Institute's CSSS2013(2013).

    [77] 毋河海. 扩展分维在地图信息综合中的应用[J]. 测绘科学, 2010,35(4):10-13. [ WuH H. Applicattion of extended fractal dimension in map generalization[J]. Science of Surveying and Mapping, 2010,35(4):10-13. ] [ Wu H H. Applicattion of extended fractal dimension in map generalization[J]. Science of Surveying and Mapping, 2010,35(4):10-13. ]

    [78] et alMultifractal to monofractal evolution of the London street network[J]. Physical Review E, 92, 062130(2015).

    [79] Modelling urban growth patterns[J]. Nature, 377, 608(1995).

    [80] Modeling urban street patterns[J]. Physical Review Letters, 100, 138702(2008).

    [81] 修春亮, 魏冶, 等. “流空间”视角的城市与区域结构[M]. 北京: 科学出版社, 2015. [ XiuC L, WeiZ, et al.Urban and regional structure from the perspective of "flow space"[M]. Beijing: Science Press, 2015. ] [ Xiu C L, Wei Z, et al. Urban and regional structure from the perspective of "flow space"[M]. Beijing: Science Press, 2015. ]

    [82] et al地理大数据为地理复杂性研究提供新机遇[J]. 地理学报, 73, 1397-1405(2018).

    [83] The infinite number of generalized dimension of fractals and strange attractors[J]. Physica D, 8, 433-435(1983).

    [84] Measuring the strangeness of strange attractors[J]. Physica D, 9, 187-190(1983).

    [85] Characterization of experimental (noisy) strange attractors[J]. Physical Review A, 29, 206-208(1984).

    [86] Collective dynamics of 'small-world' networks[J]. Nature, 393, 440-442(1998).

    [87] Emergence of scaling in random networks[J]. Science, 286, 509-512(1999).

    [88] Topology of the Italian airport network: A scale-free small-world network with a fractal structure?[J]. Chaos, Solutions and Fractals, 31, 527-536(2007).

    [89] [M]. Networks (2nd ed)(2018).

    [90] Defining dimension of a complex network[J]. Modern Physics Letters B, 21, 321-326(2007).

    [91] The correlation fractal dimension of complex networks[J]. International Journal of Modern Physics C, 24, 1350033(2013).

    [92] et alFuzzy fractal dimension of complex networks[J]. Applied Soft Computing, 25, 514-518(2014).

    [93] et alHow to calculate the fractal dimension of a complex network: The box covering algorithm[J]. Journal of Statistical Mechanics;Theory and Experiment, 2007, P03006(2007).

    [94] The size, scale, and shape of cities[J]. Science, 319, 769-771(2008).

    [95] Body size and metabolism[J]. Halgardia, 6, 315-353(1932).

    [96] Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals[J]. Proceedings of the National Academy of Sciences of the United States of America, 99, 2473-2478(2002).

    [97] Problems of relative growth[M]. London: Methuen and Co. Ltd(1932).

    [98] Die Abhängigkeit des Hirngewichts von dem Körpergewicht und den geistigen Fähigkeiten[J]. Arch. Psychiatr, 23, 436-446(1892).

    [99] [M]. On growth and form canto(1992).

    [100] Problems of relative growth (2nd ed)[M]. New York: Dover(1972).

    [101] Urban allometric growth[J]. Geografiska Annaler. HumanGeography(SeriesB), 53, 54-67(1971).

    [102] Characterizing growth and form of fractal cities with allometric scaling exponents[J]. Discrete Dynamics in Nature and Society, 1-22(2010).

    [103] The principle of allometry in biology and the social sciences[J]. General systems yearbook, 1, 76-89(1956).

    [104] An allmetric analysis of the US urban system: 1960-80[J]. Environment and Planning A: Economy and Space, 21, 463-476(1989).

    [105] Fractal dimension of a transportation network and its relationship with urban growth: A study of the Dallas-Fort Worth area[J]. Environment and Planning B: Planning and Design, 31, 895-911(2004).

    [106] A new evolutionary law[J]. Evolutionary Theory, 1, 1-30(1973).

    [107] 冯舒, 孙然好, 陈利顶. 基于土地利用格局变化的北京市生境质量时空演变研究[J]. 生态学报, 2018,38(12):4167-4179.

    [108] Ht-index for quantifying the fractal or scaling structure of geographic features[J]. Annals of the Association of American Geographers, 104, 530-540(2014).

    [109] Geospatial analysis requires a different way of thinking: The problem of spatial homogeneity[J]. GeoJournal, 80, 1-13(2015).

    [110] Head/tail breaks for visualization of city structure and dynamics[J]. Cities, 43, 69-77(2015).

    [111] Mapping block-level urban areas for all Chinese cities[J]. Annals of the American Association of Geographers, 106, 96-113(2016).

    [112] A head/tail breaks-based method for efficiently estimating the absolute boltzmann entropy of numerical raster data[J]. ISPRS International Journal of Geo-Information, 9, 103(2020).

    [113] et alCRG index: A more sensitive ht-index for enabling dynamic views of geographic features[J]. The Professional Geographer, 68, 533-545(2016).

    [114] et alUnified metrics for characterizing the fractal nature of geographic features[J]. Annals of the American Association of Geographers, 107, 1315-1331(2017).

    [115] 宋长青, 程昌秀, 杨晓帆, 等. 理解地理“耦合”实现地理“集成”[J]. 地理学报, 2020,75(1):3-13. [ SongC Q, ChengC X, YangX F. et al. Understanding geographic coupling and achieving geographic integration[J]. Acta Geographica Sinica, 2020,75(1):3-13. ] [ Song C Q, Cheng C X, Yang X F. et al. Understanding geographic coupling and achieving geographic integration[J]. Acta Geographica Sinica, 2020,75(1):3-13. ]

    [116] 张童, 姚士谋, 胡伟平, 等. 基于交通可达性的广佛都市区城市扩展的模拟与分析[J]. 地理科学, 2018,38(5):737-746.

    [117] 黎夏, 刘小平. 基于案例推理的元胞自动机及大区域城市演变模拟[J]. 地理学报, 2007,62(10):1097-1109.

    [118] et al基于核主成分元胞模型的城市演化重建与预测[J]. 地理学报, 65, 665-675(2010).

    [119] et alGlobal projections of future urban land expansion under shared socio economic pathways[J]. Nature Communications, 11, 537(2020).

    Hong ZHANG, Tian LAN, Zhilin LI. Advances in Fractal Cities: A Shift from Morphology to Network[J]. Journal of Geo-information Science, 2020, 22(4): 827
    Download Citation