Journal ArticleDOI
Packing polygons: some empirical evidence
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This article is published in Canadian Geographer.The article was published on 1980-12-01. It has received 7 citations till now.read more
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Soap, cells and statistics – random patterns in two dimensions
Denis Weaire,Nicolas Rivier +1 more
TL;DR: A survey of random two-dimensional patterns, paying particular attention to soap cell networks, metallurgical grain structures and the Giant's Causeway.
Journal ArticleDOI
Aboav-Weaire's and Lewis' laws—A review
TL;DR: A brief review of Aboav's law and Lewis' law is given in this paper, where a discussion of the mathematical forms of these two laws is discussed, with the emphasis on their mathematical forms.
Journal ArticleDOI
The spatial arrangement of random Voronoi polygons
B.N. Boots,D.J. Murdoch +1 more
TL;DR: A Monte Carlo procedure is used to derive simple models which describe some of the characteristics of the spatial arrangement of individual Voronoi polygons within a tesselation.
Journal ArticleDOI
Mean-Value Formulae for the Neighbourhood of the Typical Cell of a Random Tessellation
TL;DR: In this paper, the mean number of edges of a randomly chosen neighboring cell of the typical cell in a planar stationary tessellation, under the condition that it has n edges, has been studied by physicists for more than 20 years.
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Method of the Analysis of the Connectivity of Road and Street Network in Terms of Division of the City Area
TL;DR: The main goal of the study was to present a method of performing analysis based on the computation of numerical values of selected measures of connectivity of road and street network for a city area divided into fields of regular shape.
References
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Journal ArticleDOI
The laws of expanding circles and spheres in relation to the lateral growth of surface films and the grain-size of metals
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The arrangement of grains in a polycrystal
TL;DR: In this article, the grains of a polycrystal are found not to be disposed at random, but to be arranged in a way that can be quantitatively expressed in simple terms, and an attempt is made to relate it to a geometrical property of the intergranular surface.
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Some remarks on the arrangement of grains in a polycrystal
TL;DR: Aboav's observation of a correlation between the number of sides of a grain in a section of polycrystal and its neighbors can be explained using Euler's Theorem as discussed by the authors.
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Monte carlo estimates of the distributions of the random polygons determined by random lines in a plane
I. K. Crain,R. E. Miles +1 more
TL;DR: The results of a Monte Carlo study of the random polygons determined by homogeneous and isotropic random limes in the plane (the standard passion line process) are presented.
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The Monte-Carlo generation of random polygons
TL;DR: The approach and algorithms for the generation of random polygons are presented along with a FORTRAN program designed to generate the random Voronoi polygons, which can be adapted easily to other random polygon generations.