Rank - size rule ; zipf s law ; city - size distributions ; bi - fractals ; multifracta ls ; symmetry ; the us cities
2.
An empirical analysis is made with the population data of the us cities to verify the theory and models developed in this paper , which will contribute to reconcile the apparent difference between the hierarchical step - like frequency distribution of city sizes suggested by central place theory and the smooth curve reflected by the work on the rank - size rule
3.
In order to grasp the urban system processes and evolution pattern of hunan province comprehensively , this article has made further discussion on its structure characteristic : through regression analysis , graph analysis and statistics analysis of the time series data and cross sections data , by combining with the fractal theory , we induce the following conclusion : the hierarchical size structure presents the law of the primate city , the rank - size rule and pyramid structure characteristic , but it also has the insufficient development problem of the high hierarchical size city . by using the gravitation model , we found out that the economy relation intensity among those main cities is weak while the structure is loose . based on the urban layer system of economic development level and industrial structure evolution of the cities in hunan province , this article then induces the function combination among the five urban agglomerations in hunan province
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