Modeling the self-affine structure and optimization conditions of city systems using the idea from fractals

This paper demonstrates self-affine fractal structure of city systems by means of theoretical and empirical analyses. A Cobb-Douglas-type function (C-D function) of city systems is derived from a general urban response equation, and the partial scaling exponent of the C-D function proved to be the fractal dimension reflecting the self-affine features of city systems. As a case, the self-affine fractal model is applied to the city of Zhengzhou, China, and the result is satisfying. A fractal parameter equation indicative of structural optimization conditions is then obtained from the C-D function. The equation suggests that priority should be given to the development of the urban element with a lower fractal dimension, or a higher partial scaling exponent, for utility maximization. Moreover, the fractal dimensions of different urban elements tend to become equivalent to each other in the long term. Accordingly, it is self-similar fractals rather than self-affine fractals that represent the optimal structure of city systems under ideal conditions. (C) 2008 Elsevier Ltd. All rights reserved.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000267379700009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Mathematics, Interdisciplinary ApplicationsPhysics, MultidisciplinaryPhysics, MathematicalSCI(E)EISSCI7ARTICLE2615-6294