人文经济地理空间分数维的认知基础&mdash;&mdash;兼论分形技术的应用

宋志军

doi:10.13959/j.issn.1003-2398.2023.04.014

PDF(6648 KB)

人文地理 ›› 2023, Vol. 38 ›› Issue (4) : 121-130. DOI: 10.13959/j.issn.1003-2398.2023.04.014

经济

人文经济地理空间分数维的认知基础——兼论分形技术的应用

宋志军^1,2

作者信息 +

COGNITION BASIS OF FRACTIONAL DIMENSION IN HUMAN ECONOMIC GEOGRAPHICAL SPACE: THE APPLICATION OF FRACTAL TECHNOLOGY

SONG Zhi-jun^1,2

Author information +

文章历史 +

摘要

人文经济地理系统是复杂的开放巨系统，传统数理方法常无法描述其看似混乱的存在形式、运行过程。实际人文经济地理空间是社会经济系统相变、临界现象的终端表现，自身充满了非线性的特征和过程，所以分数维的空间形态是其本质性的系统属性。由此本文介绍了人文经济地理空间分数维的表现形式、认识过程、基本的数理描述，并对其度量方法--分形的理论基础、计算方法、应用“情境”、研究进展进行了综述和讨论。而本文对人文经济地理事物的空间分数维及分形技术所进行的溯源和应用基础讨论，其目的就是要为科学描述人文经济地理空间的复杂性、合理利用分形技术提供基础性的理论支持。

Abstract

Human economic geographical system is a complex open giant system. Traditional mathematical methods cannot explain and describe its seemingly disordered existence form and running process. In general, the monomer is in the process of change, the grassroots level shows chaos, and the macro level shows certain certainty or regularity, which constitutes the basic characteristics of the human economic geographical reality space. Compounded together, they not only enhance the complexity of the spatial system, but also become a source of fractal dimension. In fact, human economic geographical space is a final performance of phase transitions and criticality phenomenon in social economic system, and the fractal dimension is the reflection of the self-similar feature. To deeply understand this complex system full of nonlinear features and processes, this paper introduces the performance form, cognitive process and basic mathematical description of human economic geographical system. Also, this research has a summary and discussion for its measurement methods:Fractal of theoretical basis, calculation method, application "circumstance" and research development. From the mathematical point of view, fractal is mainly through the analysis of quantitative indicators with scale-free characteristics such as system singularity, evolution intensity, evolution dominance or subjectivity, to reflect irregular and difficult to measure spatial pattern changes and their evolution details.

导出引用

宋志军. 人文经济地理空间分数维的认知基础——兼论分形技术的应用[J]. 人文地理. 2023, 38(4): 121-130 https://doi.org/10.13959/j.issn.1003-2398.2023.04.014

SONG Zhi-jun. COGNITION BASIS OF FRACTIONAL DIMENSION IN HUMAN ECONOMIC GEOGRAPHICAL SPACE: THE APPLICATION OF FRACTAL TECHNOLOGY[J]. HUMAN GEOGRAPHY. 2023, 38(4): 121-130 https://doi.org/10.13959/j.issn.1003-2398.2023.04.014

中图分类号： K909

参考文献

[1] Batty M, Longley P A. Fractal Cities:A Geometry of Form and Function[M]. London:Academic Press, 1994:7-57.
[2] 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,2008:36-60.[Chen Yanguang. Fractal Urban Systems:Scaling, Symmetry, Spatial Complexity[M]. Beijing:Science Press, 2008:36-60.]
[3] Frankhauser P. Fractal geometry for measuring and modelling urban patterns[M]//Sergio Albeverio, et al. The Dynamics of Complex Urban Systems. Leipzig:Springer Books, 2008:213-243.
[4] 于渌,郝柏林,陈晓松.边缘奇迹:相变与临界现象[M].北京:科学出版社, 2016:28-162.[Yu Lu, Hao Bolin, Chen Xiaosong. Marginal Miracle:Phase Transitions and Critical Phenomena[M]. Beijing:Science Press, 2016:28-162.]
[5] 许国志.系统科学[M].上海:上海科学技术教育出版社,2000:178-180.[Xu Guozhi. System Science[M]. Shanghai:Shanghai Science and Technology Education Press, 2000:178-180.]
[6] 陈彦光.城市化:相变与自组织临界性[J].地理研究,2004,23(3):301-311.[Chen Yanguang. Urbanization as phase transition and selforganized critical process[J]. Geographical Reaearch, 2004,23(3):301-311.]
[7] 宋志军,赵欣,周德.经济地理空间的混乱现象——"熵情"——兼分析技术评述[J].经济地理,2018,38(6):35-43.[Song Zhijun, Zhao Xin, Zhou De. The chaos of economic geography:"entropy":A review of relevant analytical techniques[J]. Economic Geography, 2018,38(6):35-43.]
[8] 范冬萍.复杂系统突现论——复杂性科学与哲学的视野[M].北京:人民出版社,2011:24-47.[Fan Dongping. Emergent Theory of Complex Systems:From the Perspective of Complexity Science and Philosophy[M]. Beijing:People's Publishing House, 2011:24-47.]
[9] 冯端,冯少彤.溯源探幽:熵的世界[M].北京:科学出版社,2016:63-84.[Feng Duan, Feng Shaotong. Trace Back to the Source and Explore the Deep:The world of Entropy[M]. Beijing:Science Press, 2016:63-84.]
[10] Batty M, Morphet R, Masucci P, et al. Entropy, complexity, and spatial information[J]. Journal of Geographical Systems, 2014,16:363-385.
[11] 胡兆量,陈彦光,刘涛.经济地理面貌变化三特征[J].经济地理, 2018, 38(10):1-4.[Hu Zhaoliang, Chen Yanguang, Liu Tao. Three laws of the changes in economic geography[J]. Economic Geography, 2018,38(10):1-4.]
[12] 童维勤,黄林鹏.数据密集型计算和模型[M].上海:上海科学技术出版社,2015:1-19.[Tong Weiqin, Huang Linpeng. Data-intensive Calculations and Modeling[M]. Shanghai:Shanghai Science and Technology Press, 2015:1-19.]
[13] 陈彦光.城市规划系统工程学[M].北京:中国建筑工业出版社, 2019:81-118.[Chen Yanguang. Urban Planning Systems Engineering[M]. Beijing:China Architecture and Building Press, 2019:81-118.]
[14] Batty M, Xie Y. Self-organized criticality and urban development[J]. Discrete Dynamics in Nature and Society, 1999,3(2/3):109-124.
[15] Arthur W B. Complexity and the economy[J]. Science, 1999, 284(5411):107-109.
[16] Portugali J. Self-Organization and the City[M]. Berlin:Springer, 2000:49-72.
[17] 李忠.迭代·浑沌·分形[M].北京:科学出版社,2007:1-32.[Li Zhong. Iterative, Chaos, Fractal[M]. Beijing:Science Press, 2007:1-32.]
[18] 杰弗里·韦斯特.张培,译.规模[M].北京:中信出版集团,2018:278-329.[Geoffrey West. Zhang Pei, trans. Scale[M]. Beijing:CITIC Press Group, 2018:278-329.]
[19] Chen Y G, Feng J. Spatial analysis of cities using Renyi entropy and fractal parameters[J]. Chaos, Solitons & Fractals, 2018,105:279-287.
[20] 陈彦光.城市化与经济发展水平关系的三种模型及其动力学分析[J].地理科学,2011,31(1):1-6.[Chen Yanguang. Modelling the relationships between urbanization and economic development levels with three functions[J]. Scientia Geographica Sinica, 2011,31(1):1-6.]
[21] 陈彦光,罗静.郑州市分形结构的动力相似分析——关于城市人口、土地和产值分维关系的实证研究[J].经济地理,2001,21(4):389-393.[Chen Yanguang, Luo Jing. A dynamic similarity analysis of fractal structure of the city of Zhengzhou:An empirical study on the fractal relationship between urban population, land, and output value[J]. Economic Geography, 2001,21(4):389-393.]
[22] 陈彦光,罗静.经济系统结构与功能的分形模型——Cobb Douglas生产函数的理论来源及形式推广[J].信阳师范学院学报(自然科学版), 2000, 13(1):40-43.[Chen Yanguang, Luo Jing. General fractal models on structure and function of dynamic economy systems:The theoretical source and form extension of Cobb Douglas production function[J]. Journal of Xinyang Normal University (Natural Science Edition), 2000,13(1):40-43.]
[23] 刘春成.城市隐秩序[M].北京:社会科学文献出版社,2017:24-60.[Liu Chuncheng. The Hidden Order of City[M]. Beijing:Social Sciences Academic Press, 2017:24-60.]
[24] 孙霞,吴自勤,黄畇.分形原理及其应用[M].合肥:中国科学技术大学出版社,2003:89-142.[Sun Xia, Wu Ziqin, Huang Yun. Fractal Principle and Its Application[M]. Hefei:Press of University of Science and Technology of China, 2003:89-142.]
[25] 伊利亚·普里戈金.湛敏,译.确定性的终结[M].上海:上海科技教育出版社,2018:1-5.[Ilya Prigogine. Zhan Min, trans. The End of Certainty[M]. Shanghai:Shanghai Science and Technology Education Press, 2018:1-5.]
[26] 李水根.分形[M].北京:高等教育出版社,2004:13-79.[Li Shuigen. Fractal[M]. Beijing:Higher Education Press, 2004:13-79.]
[27] Mandelbrot B. How long is the coast of Britain? Statistical selfsimilarity and fractional dimension[J]. Science, 1967,156(3775):636-638.
[28] Chen Y G, Jiang S G. An analytical process of the spatio-temporal evolution of urban systems based on allometric and fractal ideas[J]. Chaos, Solitons & Fractals, 2009,39(1):49-64.
[29] Chen Y G. Zipf's law, 1/f noise, and fractal hierarchy[J]. Chaos, Solitons & Fractals, 2012,45(1):63-73.
[30] 陈彦光.地理数学方法:从计量地理到地理计算[J].华中师范大学学报(自然科学版),2005,39(1):113-119.[Chen Yanguang. Mathematical methods of geography:From quantitative analysis to Geocomputation[J]. Journal of Central China Normal University (Natural Science Edition), 2005,39(1):113-119.]
[31] Kantelhardt J W, Zschiegner S A, Eva K B, et al. Multifractal detrended fluctuation analysis of nonstationary time series[J]. Physica A:Statistical Mechanics and its Applications, 2002,316:87-114.
[32] Chen Y G, Wang J J. Multifractal characterization of urban form and growth:The case of Beijing[J]. Environment and Planning B:Planning and Design, 2013,40(4):884-904.
[33] Chen Y G. The solutions to the uncertainty problem of urban fractal dimension calculation[J/OL]. Entropy, 2019,21:e21050453. https://doi.org/10.3390/e21050453.
[34] Song Z J, JinW X, Jiang G H, et al. Typical and atypical multifractal systems of urban spaces:Using construction land in Zhengzhou from 1988 to 2015 as an example[J]. Chaos, Solitons & Fractals, 2021,145:110732. https://doi.org/10.1016/j.chaos.2021.110732.
[35] 张红,蓝天,李志林.分形城市研究进展:从几何形态到网络关联[J].地球信息科学学报,2020,22(4):827-841.[Zhang Hong, Lan Tian, Li Zhilin. Advances in fractal cities:A shift from morphology to network[J]. Journal of Geo-information Science, 2020,22(4):827-841.]