西北地区城市规模分形结构的研究

STUDY ON FRACTAL STRUCTURE OF CITY-SIZE OF THE NORTH-WEST REGION OF CHINA

本文利用分形理论和相空间概念，从理论的角度演绎推导出城市规模分形结构的一般模式。并以此为基础，结合西北地区自然、经济、社会状况，对五省区的城市规模分形结构进行初步分析，为深入研究其城市体系，制定城市、区域发展战略提供一定的参考。

This paper discusses fractal structure of city-size of the north-west region (including Shanxi, Gansu, Qinghai, Xinjiang Uigur Autonomous Region and Ningxia Hui Autonomous Region) in China with the purpose of revealing its characterstics and provisingreference and scientific basis for formulatiing regional developing strategies hierarchically. In the paper, fractal theory is used as a new methodology to deduce the general fractal models of city-size distribution (LnN(r) = L(A / C) - DepLn r ) whose logic process is different from the one by which some models such as Law of the primate city, Lotkarule, Zipf rule, and Parato rule, etc. based on empirical knowlege in Westem countries.Though it form is the same as Parato model, it is much richer in connotation and more than a mathematical model. In the theory, structure of city-size has no necessity to be classfied into the primate and ranksize distributions, all the types can be worked out by analysing and discussing the Kolmognorov capacity dimension (abbrev. Dcp, is also name equilibrium index, and the LnN(r) capacity onc), a measurement of the stuffing unit's ability to stuff the phase spatiality of the city size.The more the valuc of Dcp is, the more concentrated the city-size distribution becomes, and the more equilibrated the city system is. And correspondingly, the medium and small cities are more developed, and the hierarchical city system is at the developing stage. lt is reverse on the reverse.(1) Lim Dcp = ∞, all the cities are the same in size;(2) Lim Dcp = 0, there is only one city in the so-called city system;(3)When the Dcp is at the broken point between fraction and integer (i.e. Lim Dcp = 1), the city system is in the medium situation, abiding by Zipf rule. Integrating with GM(1,1 ), a forcasting model of the grey system, the paper analyses the characteristics of the fractal structure of city-size of the northwest region of China temporally and spatially, and draw a conclusion as the following:(1) The status quo.Shanxi, Gansu and Xinjiang have the high Dcps, while the urbanization of Qinghai and Ningxia is at the early stage. Taking the northwest region as a whole, the big cities are developing rapidly, while the medium and smill cities are insufficient. Therefore, this paper bring out the total strategy of urban development that the expansion of big cities should be under control, while medium cities should be developed appropriately and small cities achvely.(2)Temporal distribution. Though the northwest region is facing a rising tendcncy in Dcp, there is difference for provinces and antonomous region in velocity; Shanxi and Xinjiang are fast, while Gansu and Ningxia are correspondingly slow.(3) Sptial distrubution. At present, Shanxi, Gansu and Xinjiang, the major part of the famous old 'Silk Road', on an aspect of the 'fractal dimension ridge',while Qinghai and Ningxia present a 'fractal dimension valley', According to the results of forcasting, a regional pattern of 'fractal dimension saddle' will become clearer and clcarer because of Gansu's slowness in urbanzation. This will make negtive effect not only on Gansu province itself, but a1so onXinjiang and the whole northwest region, and even worse tbe coming national strategic shift.(4) Qinghai and Ningxia are suggested to be brought into a high hierarchicalcity system for their laggness in development of structure of city-size and insufficient ability of self-development.