Aggregate and fractal tessellations View Full Text


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Article Info

DATE

2001-10

AUTHORS

Konstantin Tchoumatchenko, Sergei Zuyev

ABSTRACT

Consider a sequence of stationary tessellations {Θn}, n=0,1,…, of ℝd consisting of cells {Cn(xin)}with the nuclei {xin}. An aggregate cell of level one, C01(xi0), is the result of merging the cells of Θ1 whose nuclei lie in C0(xi0). An aggregate tessellation Θ0n consists of the aggregate cells of level n, C0n(xi0), defined recursively by merging those cells of Θn whose nuclei lie in Cn−1(xi0). We find an expression for the probability for a point to belong to atypical aggregate cell, and obtain bounds for the rate of itsexpansion. We give necessary conditions for the limittessellation to exist as n→∞ and provide upperbounds for the Hausdorff dimension of its fractal boundary and forthe spherical contact distribution function in the case ofPoisson-Voronoi tessellations {Θn}. More... »

PAGES

198-218

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/pl00008802

DOI

http://dx.doi.org/10.1007/pl00008802

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1053393745


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