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Aggregate and Fractal Tessellations

Abstract : Consider a sequence of stationary tessellations {Theta^n, n=0,1,...} of R^d consisting of cells {C^n(x_i^n)} with the nuclei {x_i^n}. An aggregate cell of level one, C_0^1(x_i^0), is the result of merging the cells of Theta^1 whose nuclei lie in C^0(x_i^0). An aggregate tessellation Theta_0^n consists of the aggregate cells of level n, C_0^n(x_i^0), defined recursively by merging those cells of Theta^n whose nuclei lie in C_0^n-1(x_i^0). We find an expression for the probability for a point to belong to a typical aggregate cell and obtain bounds for the probability of cell's expansion and extinction. We give necessary conditions for the limit tessellation to exist as n to infinity and provide upper bounds for the Hausdorff dimension of its fractal boundary and for the spherical contact distribution function in the case of Poisson-Voronoi tessellations {Theta^n}.
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Submitted on : Wednesday, May 24, 2006 - 11:29:32 AM
Last modification on : Friday, February 4, 2022 - 3:18:47 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:29:49 PM


  • HAL Id : inria-00072969, version 1



Konstantin Tchoumatchenko, Sergei Zuyev. Aggregate and Fractal Tessellations. RR-3699, INRIA. 1999. ⟨inria-00072969⟩



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