Fractal dimension evolution and spatial replacement dynamics of urban   growth

doi:10.1016/j.chaos.2011.10.007

CORC > 北京大学 > 城市与环境学院

	Fractal dimension evolution and spatial replacement dynamics of urban growth
	Chen, Yanguang
刊名	chaos solitons fractals
	2012
关键词	SHAPE FORM BRUSSELS GEOMETRY INDEXES CITIES AREAS SIZE
DOI	10.1016/j.chaos.2011.10.007
英文摘要	This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to interpret the fractal dimension of urban form. The fractal dimension evolution of urban growth can be empirically modeled with Boltzmann's equation. For the normalized data, Boltzmann's equation is just equivalent to the logistic function. The logistic equation can be transformed into the well-known 1-dimensional logistic map, which is based on a 2-dimensional map suggesting spatial replacement dynamics of city development. The 2-dimensional recurrence relations can be employed to generate the nonlinear dynamical behaviors such as bifurcation and chaos. A discovery is thus made in this article that, for the fractal dimension growth following the logistic curve, the normalized dimension value is the ratio of space filling. If the rate of spatial replacement (urban growth) is too high, the periodic oscillations and chaos will arise. The spatial replacement dynamics can be extended to general replacement dynamics, and bifurcation and chaos mirror a process of complex replacement. (C) 2011 Elsevier Ltd. All rights reserved.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000301019800002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Interdisciplinary Applications; Physics, Multidisciplinary; Physics, Mathematical; SCI(E); EI; SSCI; 11; ARTICLE; 2; 115-124; 45
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/161050]
专题	城市与环境学院
推荐引用方式 GB/T 7714	Chen, Yanguang. Fractal dimension evolution and spatial replacement dynamics of urban growth[J]. chaos solitons fractals,2012.
APA	Chen, Yanguang.(2012).Fractal dimension evolution and spatial replacement dynamics of urban growth.chaos solitons fractals.
MLA	Chen, Yanguang."Fractal dimension evolution and spatial replacement dynamics of urban growth".chaos solitons fractals (2012).