基于分形的城市体系经济规模等级研究

利用分形理论进行城市体系的经济规模等级特征分析，推广了规模等级分形理论的应用领域。以长江三角洲地区县级以上行政单位为研究对象，以2009年经济数据为载体，分别从分部门的经济总量、经济密度和第一无标度区3个角度计算了城市体系经济规模的分维，验证了分形理论在城市体系经济规模等级研究中的适用性。结果表明：（1）城市体系中的经济规模等级呈现较好的分形特征，分形维数可以作为城市体系经济规模等级研究的有力工具；（2）长江三角洲地区当前各经济社会部门的规模等级特征差异较大，中心城市垄断性较强；（3）长江三角洲地区经济规模等级层次明显；（4）以无标度区为基础可以将长江三角洲地区划分为核心经济区和经济发展边缘区

LEVEL OF ECONOMIC SCALE OF URBAN SYSTEM BASED ON FRACTAL

At present,the application of fractal theory in the grade scale of urban system is mainly focus on revealing the space distribution features of population scale and land use scale.As the main push factors of population scale and land use scale,the distribution regulation of the grade on economic scale in urban system is still researched seldom.The distribution regulation of the grade on economic scale is the decisive factors for the further development direction of the urban system.Exploring the distribution regulation of the grade on economic scale is helpful to understand the reasons why different cities play different economic roles in the urban system.With the fractal theory,this paper analyzed the characteristics of the features of the grade on economic scale of each city in urban system.Selecting the administrative units above the county level in the Yangtze River Delta as example,we calculated the fractal dimension of the economic scale of the regional urban system separately from the total economy,economic density and scaling range based on the statistical data of 2009.The result showed as follows.(1) The space distribution of the grade scale of economies in urban system had a good fractal feature.In the computation of the fractal dimension for the overall sample,all computing projects basically met the R2>0.95,the proportion of 134 subjects included in the scaling range was also great.In the scaling range stratified study,correlation coefficients of the first scaling range were all above 098,most of correlation coefficients of the second and the third scaling range were above 095.The fractal characteristics were very obvious.(2) At present,there was a great difference in the spatial patterns of economic and social departments in the Yangtze River Delta.The monopoly of the central city was becoming stronger.Even though the difference of the total economic output tended to be relatively small, the economic density turned to be relatively large.The distributions of the first industry were more uniform,but the fractal dimension of the secondary industry and tertiary industry which dominated the GDP showed obvious characteristics of dispersion.In the pull factors of social economy,the factors in addition to the fixed assets investments with slightly uniform characteristics showed obvious scattered characteristics.Monopoly role of central cities was very obvious from the strength of the external economic links to spending power.(3) The economic scale hierarchy was obvious in the Yangtze River Delta.(4) Based on the features of scaling ranges,the Yangtze River Delta could be divided into two types of areas.The areas entered into the first scaling range were core economic region.The areas that had not entered into the first scaling range were marginal economic region.(5) This paper verified the applicability of the fractal dimension on the study of economic scales of urban system.It shows that the fractal dimension is more effective in discussing the distributions of all industry scales of the urban system,thus we can analyze the current social and economic development of the Yangtze River Delta