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Reports Year : 1999

Aggregate and Fractal Tessellations


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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Dates and versions

inria-00072969 , version 1 (24-05-2006)


  • HAL Id : inria-00072969 , version 1


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