A set of formulae on fractal dimension relations and its application to   urban form

doi:10.1016/j.chaos.2013.07.010

CORC > 北京大学 > 城市与环境学院

	A set of formulae on fractal dimension relations and its application to urban form
	Chen, Yanguang
刊名	chaos solitons fractals
	2013
关键词	SELF-ORGANIZED CRITICALITY DIFFUSION-LIMITED AGGREGATION CELLULAR-AUTOMATA LAND-USE AREA MORPHOLOGY GROWTH DYNAMICS PATTERNS GEOMETRY
DOI	10.1016/j.chaos.2013.07.010
英文摘要	The area-perimeter scaling can be employed to evaluate the fractal dimension of urban boundaries. However, the formula in common use seems to be not correct. By means of mathematical method, a new formula of calculating the boundary dimension of cities is derived from the idea of box-counting measurement and the principle of dimensional consistency in this paper. Thus, several practical results are obtained as follows. First, I derive the hyperbolic relation between the boundary dimension and form dimension of cities. Using the relation, we can estimate the form dimension through the boundary dimension and vice versa. Second, I derive the proper scales of fractal dimension: the form dimension comes between 1.5 and 2, and the boundary dimension comes between I and 1.5. Third, I derive three form dimension values with special geometric meanings. The first is 4/3, the second is 3/2, and the third is 1 + 2(1/2)/2 approximate to 1.7071. The fractal dimension relation formulae are applied to China's cities and the cities of the United Kingdom, and the computations are consistent with the theoretical expectation. The formulae are useful in the fractal dimension estimation of urban form, and the findings about the fractal parameters are revealing for future city planning and the spatial optimization of cities. (C) 2013 Elsevier Ltd. All rights reserved.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000324442600016&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Interdisciplinary Applications; Physics, Multidisciplinary; Physics, Mathematical; SCI(E); EI; 1; ARTICLE; 150-158; 54
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/160964]
专题	城市与环境学院
推荐引用方式 GB/T 7714	Chen, Yanguang. A set of formulae on fractal dimension relations and its application to urban form[J]. chaos solitons fractals,2013.
APA	Chen, Yanguang.(2013).A set of formulae on fractal dimension relations and its application to urban form.chaos solitons fractals.
MLA	Chen, Yanguang."A set of formulae on fractal dimension relations and its application to urban form".chaos solitons fractals (2013).