Journal ArticleDOI
Preliminary evidence for a theory of the fractal city.
Michael Batty,Yichun Xie +1 more
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It is argued that the geometry of urban residential development is fractal, and two methods for estimating fractal dimension based on varying the size of cities and the scale at which their form is detected are introduced.Abstract:
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...read more
Citations
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The use of remote sensing and landscape metrics to describe structures and changes in urban land uses
TL;DR: In this article, the authors used information on image spatial formlandscape metricsto describe urban land-use structures and land-cover changes that result from urban growth, based on spatial analysis of landcover structures mapped from digitally classified aerial photographs of the urban region Santa Barbara, CA.
Journal ArticleDOI
Fractal dimension and fractal growth of urbanized areas
TL;DR: This paper computes planar fractal dimensions of 20 large US cities along with their surrounding urbanized areas and explores fractal dimension and fractal growth of Baltimore, MD for the 200-year span from 1792–1992.
Journal ArticleDOI
Urban Evolution on the Desktop: Simulation with the Use of Extended Cellular Automata
TL;DR: The author poses the need to develop simple simulations which emphasise the conditions under which spontaneous growth, such as that which characterises the regeneration of inner cities and the location of edge cities, can be modelled.
Journal ArticleDOI
The morphology of built-up landscapes in Wallonia (Belgium): A classification using fractal indices
TL;DR: In this article, the spatial pattern of built-up areas within a NUTS-1 European region (Wallonia in Belgium) is analyzed using fractal indices, and an expectation maximisation algorithm (EM) combined with a Bayesian information criterion (BIC) is used.
Journal Article
Multi-Scale Fractal Analysis of Image Texture and Pattern
TL;DR: In this article, the fractal dimension of a remotely sensed image was measured to investigate the relationship between texture and resolution for different land covers in the vicinity of Huntsville, Alabama.
References
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Journal ArticleDOI
A Computer Movie Simulating Urban Growth in the Detroit Region
TL;DR: A Computer Movie Simulating Urban Growth in the Detroit Region as discussed by the authors was made to simulate urban growth in the city of Detroit, Michigan, United States of America, 1970, 1970.
Book
Fractal Cities: A Geometry of Form and Function
Michael Batty,Paul A. Longley +1 more
TL;DR: Planners and architects will find that many aspects of fractal geometry covered in this book are relevant to their own interests.
Journal ArticleDOI
Urban Growth and Form: Scaling, Fractal Geometry, and Diffusion-Limited Aggregation
TL;DR: The diffusion-limited aggregation (DLA) model as mentioned in this paper generates highly ramified tree-like clusters of particles, or populations, with evident self-similarity about a fixed point and the extent to which such clusters fill space is measured by their fractal dimension which is estimated from scaling relationships linking population and density to distances within the cluster.
Journal ArticleDOI
Form follows function: reformulating urban population density functions.
Michael Batty,Kwang Sik Kim +1 more
TL;DR: In this paper, the authors argue that the most appropriate form for urban population density models is the inverse power function, contrary to conventional practice, which is largely based upon the negative exponential.