Spatial pattern and fractal characteristics of producer services' external function in China

Abstract

Using the Zipf's law and differentiated index, we analyze the spatial pattern, size hierarchy and fractal evolution of producer services' external function at provincial and city scales of China from 2003 to 2011, which are based on urban basic economic theory.Conclusions can be drawn as follows: The external functions of China's producer services have significantly differences, which show a trend of polarization at different scales, and widen the gaps among the external functions of different provinces and cities. At provincial scale, nine provincial units which are Xinjiang, Shandong, Henan, Hubei, Chongqing, Guizhou, Yunnan,Jiangxi and Fujian, do not have external function; at city scale, they generate a number of intensive areas of external function, which are mainly in the northeastern China and eastern coastal China and present different spatial structures and obvious changes in the characteristics,that is to say, the spatial hierarchical structure in the eastern China is better than that in the central and western China. The rank- size distributions of the producer services' external function at provincial and city scales comply with Zipf's law, however, they are characterized by single fractal at provincial scale and dual fractals at city scale; the grade equilibrium of the external service flow in the first scale area is slightly better than that at the provincial scale.The second and ineffective scale areas are central centers of local service, showing a significant change in the internal structure of the system and widening the gap among the urban external functions. External function cities can be divided into five types of service centers. High-grade service centers' external function are improving faster than that of other types, and the gaps are widening among different size hierarchy service centers.