Preliminary evidence for a theory of the fractal city
Preliminary evidence for a theory of the fractal city
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DOI：
10.1068/a281745
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发表时间：
1996-10-01
期刊：
影响因子：
--
通讯作者：
Xie, Y
中科院分区：
文献类型：
--
作者：
Batty, M;Xie, Y
本文认为城市住宅发展的几何形态是分形的。空间被填充的程度和填充的速度都遵循尺度规律，这意味着功能的不变性和城市形态在尺度上的自相似性。这些特征被捕获在基于逆幂律的人口密度函数中，其参数是分形维数。首先，我们从尺度关系的角度概述了分形维数理论的相关要素，然后介绍了两种基于城市规模和城市形态检测尺度变化的分形维数估计方法。每种方法分别采用精确估计和统计估计技术，产生测量空间填充程度和填充速率的维度。然后将这些方法应用于美国东北部六个工业城市的住宅开发模式，并使用来自TIGER/Line文件的创新数据源。研究结果支持了Batty、Longley和Frankhauser在书中提出的分形城市理论，但明确的结论是，不同的尺度和估计技术会产生不同类型的分形维数。
In this paper, we argue that the geometry of urban residential development is fractal. Both the degree to which space is filled and the rate at which it is filled follow scaling laws which imply invariance of function, and self-similarity of urban form across scale. These characteristics are captured in population density functions based on inverse power laws whose parameters are fractal dimensions. First we outline the relevant elements of the theory in terms of scaling relations and then we introduce two methods for estimating fractal dimension based on varying the size of cities and the scale at which their form is detected. Exact and statistical estimation techniques are applied to each method respectively generating dimensions which measure the extent and the rate of space filling. These methods are then applied to residential development patterns in six industrial cities in the northeastern United States, with an innovative data source from the TIGER/Line files. The results support the theory of the fractal city outlined in books by Batty and Longley and Frankhauser, but with the clear conclusion that different scale and estimation techniques generate different types of fractal dimension.