Original Articles

Study on Fractal Model of Regional Urban Pole-Axis System Spatial Structure

  • 1. School of Land Science and Technology, China University of Geosciences, Beijing 100083, China; |
    2. Beijing Key Laboratory of Land Resources Information Development Research, Beijing 100083, China

Online published: 2009-11-25


Pole-axis system is one of the main modes of Chinese regional spatial structure. It is an academic element for geographical space optimization to research urban pole-axis system spatial structure and reveal its mathematics nature. Based on pole-axis system theory, a fractal model of pole-axis system was built, and then its geographical meaning was illuminated. According to the mathematic elements of pole-axis system fractal model, this paper developed counting program of fractal model by GIS software. Taking urban-traffic system in Jinan City, Shandong Province as an example, this paper counted the parameter of its fractal model by using GIS data format. The results showed that: (1) The pole-axis system presented a fractal nature indeed when developing to a certain stage, and the fractal model of pole-axis system can effectively reflect the spatial structure of pole-axis system. (2) Fractal, scale-free and order is the different states of geo-spatial. We deduced that its spatial structure has experienced an iterative process of disorder → scale-free → fractal→ order→ a more complex disorder with the development of pole-axis system. (3) The urban-traffic system in Jinan City, Shandong Province had shaped the rudimental structure of pole-axis system, which was in the developing stage.

Cite this article

MENG Lina1, ZHENG Xinqi1,2, ZHAO Lu1, LI Zhijian1, YANG Xin1 . Study on Fractal Model of Regional Urban Pole-Axis System Spatial Structure[J]. PROGRESS IN GEOGRAPHY, 2009 , 28(6) : 944 -951 . DOI: 10.11820/dlkxjz.2009.06.016


[1]  Volchenkov D , Blanchard P H. Scaling and universality in city space syntax: between Zipf and Matthew. Physica A: Statistical Mechanics and its Applications, 2008, 387(10): 2353-2364.

[2]   Michele G, Funaro M. Topology of the Italian airport network: A scale-free small-world network with a fractal structure. Chaos, Solitons & Fractals, 2007, 31(3): 527-536.

[3]   陈彦光,王义民,靳军. 城市空间网络:标度、对称、复杂与优化——城市体系空间网络分形结构研究的理论总结报告. 信阳师范学院学报(自然科学版), 2004,17(3):311-317.

[4]   陆大道. 关于“点—轴”空间结构系统的形成机理分析. 地理科学,2002,22(1):1-6.

[5]   克里斯塔勒. 德国南部中心地原理. 常正文译. 北京:商务印书馆,1998.

[6]   陆大道. 区域发展及其空间结构. 北京:科学出版社,1995.

[7]   White R, Engelen G. Celluar automata and fractal urban form: a celluar modeling approach to the evolution of urban land-use pattern. environment and planning A, 25: 1175-1191.

[8]   陈彦光. 中心地体系空间结构的标度定律与分形模型: 对Christaeller中心地模型的数学抽象与理论推广. 北京大学学报(自然科学版),2004,40(4):626-734.

[9]   陈彦光,周一星. 基于三角点阵模型的自组织城市网络探讨. 北京大学学报(自然科学版),2005,41(2):258-264.

[10] Batty M, Longley P A. Urban shapes as fractals. Area, 1987, 19: 215-221.

[11] Allen P M, Sanglier M. Urban evolution, self-organization and dicision making. Enrionment and Planning A, 1981, 13: 169-183.

[12] J Portugali. Self-organization and the City. Berlin: Spring–Verlag, 2000.

[13] Frankhauser P. La fractalite des structures urbains. Pairs: Collection Villes, Anthropos, 1994.

[14] White R, Engelen G. Urban system dynamics and cellular automata: Fractal structures between order and chaos. Chaos, Solitons and Fractals, 1994, 4: 563-583.

[15] Helbing D, Keltsch J, Molnar P. Modelling the evolution of human trail systems. Nature, 1997, 388(6637): 47-50.

[16] 刘继生,陈彦光. 城市、分形与空间复杂性探索. 复杂系统与复杂性科学,2004,1(3):62-69.

[17]陆玉麒. 论点—轴系统理论的科学内涵. 地理科学,2002,22(4):136-143.

[18] 刘继生,陈彦光,刘志刚. 点—轴系统的分形结构及其空间复杂性探讨. 地理研究,2003,22(4):447-454.

[19] 杨吾扬. 区位论原理. 兰州:甘肃人民出版社,1989.

[20] 陆大道. 论区域的最佳结构与最佳发展: 提出“点—轴系统”和“T”型结构以来的回顾与再分析. 地理学报,2001,56(2):127-135.

[21] 徐建华. 现代地理学中的数学方法. 北京:高等教育出版社,2002.

[22]陈涛. 城镇体系随机聚集的分形研究. 科技通报,1995(2):98-101.

[23] 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. 1999,18(2):171-178.

[24] 车宏安,顾基发. 无标度网络及其系统科学意义. 系统工程理论与实践,2004(4):11-16.

[25] 王林,戴冠中. 复杂网络的度分布研究. 西北工业大学学报,2006,24(4):405-409.

[26]伍世代,王强. 福建省城镇体系分形研究. 地理科学,2007,27(4):493-498.

[27] 陈彦光,罗静.河南省城市—交通网络的分形特征.信阳师范学院学报(自然科学版),1998,11(2):171-177.

[28] 刘继生,陈彦光. 交通网络空间结构的分形维数及其测算方法探讨. 地理学报,1999,54(5):471-478.

[29] 郑新奇,王爱萍,李新运. 基于空间数据库的分形计算方法改进软件设计. 科学研究月刊,2006,(2):1-3.

[30] Chen Chingju, Lee Tzongyeang, Huang Y M, et al. Extraction of characteristic points and its fractal reconstruction for terrain profile data. Chaos, Solitons & Fractals, 2009, 39(4): 1732-1743.

[31] Fritzke Bernd, Erkki Oja, Samuel Kaski. Kohonen maps
[M/OL]. Amsterdam: Elsevier science B. V. 1999: 131-144
[2009-4-26]. http://www.sciencedirect.com/science/article/B8559-4NXB839-S/2/a41a2165b7c53a38e61d79745 a4dd1ac.

[32] Baas, Andreas C W. Fractal and self-organization in    coastal geomorphology: Simulating dune landscape in vegetated environments. Geomorphology, 2002,48(1): 309-328.

[33] Wilson A G. Complex spatial system: Challenges for modelers. Mathematical and Computer Modeling, 2002, 36(3): 379-387.