PROGRESS IN GEOGRAPHY ›› 2017, Vol. 36 ›› Issue (5): 529-539.doi: 10.18306/dlkxjz.2017.05.001
• Reviews • Next Articles
Received:
2016-05-01
Online:
2017-05-20
Published:
2017-05-20
Supported by:
Yanguang CHEN. Approaches to estimating fractal dimension and identifying fractals of urban form[J].PROGRESS IN GEOGRAPHY, 2017, 36(5): 529-539.
[1] | 陈彦光. 1998. 中心地体系中的分形和分维[J]. 人文地理, 13(3): 19-24, 18. |
[Chen Y G.1998. Fractals and fractal dimensions in central place systems[J]. Human Geography, 13(3): 19-24, 18.] | |
[2] | 陈彦光. 2008. 分形城市系统: 标度·对称·空间复杂性[M]. 北京: 科学出版社. |
[Chen Y G.2008. Fractal urban systems: Scaling, symmetry, spatial complexity[M]. Beijing, China: Science Press.] | |
[3] | 陈彦光. 2015. 简单、复杂与地理分布模型的选择[J]. 地理科学进展, 34(3): 321-329. |
[Chen Y G.2015. Simplicity, complexity, and mathematical modeling of geographical distributions[J]. Progress in Geography, 34(3): 321-329.] | |
[4] | 陈彦光, 刘继生. 2007. 城市形态分维测算和分析的若干问题[J]. 人文地理, 22(3): 98-103. |
[Chen Y G, Liu J S.2007. On fractal dimension calculation and analysis of urban form[J]. Human Geography, 22(3): 98-103.] | |
[5] | 陈彦光, 张莉. 2014. 信阳城市人口—城区用地异速生长分析[J]. 地理科学进展, 33(8): 1058-1067. |
[Chen Y G, Zhang L.2014. An allometric analysis of the scaling relations between population and urban area of Xinyang[J]. Progress in Geography, 33(8): 1058-1067.] | |
[6] |
姜世国, 周一星. 2006. 北京城市形态的分形集聚特征及其实践意义[J]. 地理研究, 25(2): 204-212.
doi: 10.3321/j.issn:1000-0585.2006.02.003 |
[Jiang S G, Zhou Y X.2006. The fractal urban form of Beijing and its practical significance[J]. Geographical Research, 25(2): 204-212.]
doi: 10.3321/j.issn:1000-0585.2006.02.003 |
|
[7] | 刘继生, 陈彦光. 1998. 城镇体系等级结构的分形维数及其测算方法[J]. 地理研究, 17(1): 82-89. |
[Liu J S, Chen Y G.1998. Fractal dimensions of hierarchical structure of urban systems and the methods of their determination[J]. Geographical Research, 17(1): 82-89.] | |
[8] |
刘继生, 陈彦光. 1999a. 城镇体系空间结构的分形维数及其测算方法[J]. 地理研究, 18(2): 171-178.
doi: 10.3321/j.issn:1000-0585.1998.01.012 |
[Liu J S, Chen Y G.1999a. Fractal dimensions of spatial structure of an urban system and the methods of their determination[J]. Geographical Research, 18(2): 171-178.]
doi: 10.3321/j.issn:1000-0585.1998.01.012 |
|
[9] |
刘继生, 陈彦光. 1999b. 交通网络空间结构的分形维数及其测算方法探讨[J]. 地理学报, 54(5): 471-478.
doi: 10.3321/j.issn:0375-5444.1999.05.011 |
[Liu J S, Chen Y G.1999b. A study on fractal dimensions of spatial structure of transport networks and the methods of their determination[J]. Acta Geographica Sinica, 54(5): 471-478.]
doi: 10.3321/j.issn:0375-5444.1999.05.011 |
|
[10] | 刘继生, 陈彦光. 2003. 河南省城镇体系空间结构的多分形特征及其与水系分布的关系探讨[J]. 地理科学, 23(6): 713-720. |
[Liu J S, Chen Y G.2003. Multifractal measures based on man-land relationships of the spatial structure of the urban system in Henan[J]. Scientia Geographica Sinica, 23(6): 713-720.] | |
[11] |
秦静, 方创琳, 王洋, 等. 2015. 基于三维计盒法的城市空间形态分维计算和分析[J]. 地理研究, 34(1): 85-96.
doi: 10.11821/dlyj201501008 |
[Qin J, Fang C L, Wang Y, et al.2015. A three dimensional box-counting method for estimating fractal dimension of urban form[J]. Geographical Research, 34(1): 85-96.]
doi: 10.11821/dlyj201501008 |
|
[12] | Addison P S.1997. Fractals and chaos: An illustrated course[M]. Bristol, Philadelphia: Institute of Physics Publishing. |
[13] |
Ariza-Villaverde A B, Jiménez-Hornero F J, De Ravé E G.2013. Multifractal analysis of axial maps applied to the study of urban morphology[J]. Computers, Environment and Urban Systems, 38: 1-10.
doi: 10.1016/j.compenvurbsys.2012.11.001 |
[14] | Bak P.1996. How nature works: The science of self-organized criticality[M]. New York, NY: Springer-Verlag. |
[15] | Batty M, Longley P.1994. Fractal cities: A geometry of form and function[M]. London, UK: Academic Press. |
[16] |
Benguigui L, Czamanski D, Marinov M, et al.2000. When and where is a city fractal[J] Environment and Planning B: Planning and Design, 27(4): 507-519.
doi: 10.1068/b2617 |
[17] |
Chen Y G, Wang J J.2013. Multifractal characterization of urban form and growth: The case of Beijing[J]. Environment and Planning B: Planning and Design, 40(5): 884-904.
doi: 10.1068/b36155 |
[18] |
De Keersmaecker M-L, Frankhauser P, Thomas I.2003. Using fractal dimensions for characterizing intra-urban diversity: The example of Brussels[J]. Geographical Analysis, 35(4): 310-328.
doi: 10.1353/geo.2003.0014 |
[19] | Feder J.1988. Fractals[M]. New York, NY: Plenum Press: 11. |
[20] |
Feng J, Chen Y G.2010. Spatiotemporal evolution of urban form and land-use structure in Hangzhou, China: Evidence from fractals[J]. Environment and Planning B: Planning and Design, 37(5): 838-856.
doi: 10.1068/b35078 |
[21] | Frankhauser P.1994. La Fractalité des structures urbaines (the fractal aspects of urban structures)[M]. Paris, France: Economica. |
[22] |
Frankhauser P.1998. The fractal approach. A new tool for the spatial analysis of urban agglomerations[J]. Population: An English Selection, 10(1): 205-240.
doi: 10.2307/1534622 |
[23] | Jullien R, Botet R.1987. Aggregation and fractal aggregates[M]. Singapore: World Scientific Publishing. |
[24] | Kaye B H.1989. A random walk through fractal dimensions[M]. New York, NY: VCH Publishers. |
[25] |
Mandelbrot B B.1967. How long is the coast of Britain? Statistical self-similarity and fractional dimension[J]. Science, 156: 636-638.
doi: 10.1126/science.156.3775.636 pmid: 17837158 |
[26] | Mandelbrot B B.1977. Fractals: Form, chance, and dimension[M]. San Francisco, CA: W. H. Freeman and Company. |
[27] | Mandelbrot B B.1983. The fractal geometry of nature[M]. New York, NY: W. H. Freeman and Company. |
[28] |
Murcio R, Masucci A P, Arcaute E, et al.2015. Multifractal to monofractal evolution of the London street network[J]. Physical Review E, 92(6): 062130.
doi: 10.1103/PhysRevE.92.062130 pmid: 26764655 |
[29] | Shelberg M C, Moellering H, Lam N.1982. Measuring the fractal dimensions of empirical cartographic curves[J]. Auto Carto, 5: 481-490. |
[30] |
Shen G Q.2002. Fractal dimension and fractal growth of urbanized areas[J]. International Journal of Geographical Information Science, 16(5): 419-437.
doi: 10.1080/13658810210137013 |
[31] |
Thomas I, Frankhauser P, Biernacki C.2008. The morphology of built-up landscapes in Wallonia (Belgium): A classification using fractal indices[J]. Landscape and Urban Planning, 84(2): 99-115.
doi: 10.1016/j.landurbplan.2007.07.002 |
[32] |
Thomas I, Frankhauser P, De Keersmaecker M-L.2007. Fractal dimension versus density of built-up surfaces in the periphery of Brussels[J]. Papers in Regional Science, 86(2): 287-308.
doi: 10.1111/j.1435-5957.2007.00122.x |
[33] | Vicsek T.1989. Fractal growth phenomena[M]. Singapore: World Scientific Publishing. |
[34] |
White R, Engelen G.1994. Urban systems dynamics and cellular automata: Fractal structures between order and chaos[J]. Chaos, Solitons & Fractals, 4(4): 563-583.
doi: 10.1016/0960-0779(94)90066-3 |
[1] | Limin JIAO, Chen GONG, Gang XU, Ting DONG, Boen ZHANG, Zehui LI. Urban expansion dynamics and urban forms in three metropolitan areas—Tokyo, New York, and Shanghai [J]. PROGRESS IN GEOGRAPHY, 2019, 38(5): 675-685. |
[2] | Shan LIANG, Yu DENG, Ning JIA, Yi LIU. Impact of urban morphology on sewage systems based on a virtual city modeling approach [J]. PROGRESS IN GEOGRAPHY, 2019, 38(3): 441-451. |
[3] | Yao XIONG, Runqiu PAN, Gang XU, Limin JIAO, Kai LI. A comparison of spatial and temporal characteristics of urban expansion in India during 1990-2014 [J]. PROGRESS IN GEOGRAPHY, 2019, 38(2): 271-282. |
[4] | Yanguang CHEN. Monofractal, multifractals, and self-affine fractals in urban studies [J]. PROGRESS IN GEOGRAPHY, 2019, 38(1): 38-49. |
[5] | Linshan HUANG, Yanguang CHEN, Shuangcheng LI. Multifractal spectral analysis of land use structure of the Beijing-Tianjin-Hebei urban system [J]. PROGRESS IN GEOGRAPHY, 2019, 38(1): 50-64. |
[6] | Jingtian ZHAO, Yanguang CHEN, Shuangcheng LI. Bi-fractal structure and evolution of the Beijing-Tianjin-Hebei region urban land-use patterns [J]. PROGRESS IN GEOGRAPHY, 2019, 38(1): 77-87. |
[7] | Yuqing LONG, Yanguang CHEN. Multi-scaling allometric analysis of the Beijing-Tianjin-Hebei urban system based on nighttime light data [J]. PROGRESS IN GEOGRAPHY, 2019, 38(1): 88-100. |
[8] | Feng ZHANG, Yanguang CHEN, Xiaosong LI. Radial dimension analysis of growth and form of cities in the Beijing-Tianjin-Hebei region [J]. PROGRESS IN GEOGRAPHY, 2019, 38(1): 65-76. |
[9] | Yanguang CHEN. Simplicity, complexity, and mathematical modeling of geographical distributions [J]. PROGRESS IN GEOGRAPHY, 2015, 34(3): 321-329. |
[10] | Xingye TAN, Yanguang CHEN. Urban boundary identification based on neighborhood dilation [J]. PROGRESS IN GEOGRAPHY, 2015, 34(10): 1259-1265. |
[11] | Yanguang CHEN, Li ZHANG. An allometric analysis of the scaling relations between population and urban area of Xinyang [J]. PROGRESS IN GEOGRAPHY, 2014, 33(8): 1058-1067. |
[12] | WANG Huifang, ZHOU Kai. Review of urban form, structure and morphology in China during 2003-2013 [J]. PROGRESS IN GEOGRAPHY, 2014, 33(5): 689-701. |
[13] | ZHANG Jing, PU Lijie, ZHU Ming, XU Yan, LI Peng. Comparison of land-use structure fractal dimension based on vector and raster data: A case study of Suzhou City [J]. PROGRESS IN GEOGRAPHY, 2013, 32(6): 932-939. |
[14] | YIN Changying, SHI Yishao, WANG Hefeng. Process and characteristics of boundary expansion of built-up area of Shanghai City since the late Qing dynasty [J]. PROGRESS IN GEOGRAPHY, 2013, 32(12): 1793-1803. |
[15] | WANG Shijun, WANG Yongchao, FENG Zhangxian. Spatial Relationships Between Central Places in the Central Region of Jilin [J]. PROGRESS IN GEOGRAPHY, 2012, 31(12): 1628-1635. |
|