HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Reports

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}.
Document type :
Reports
Complete list of metadata

https://hal.inria.fr/inria-00072969
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
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

Identifiers

  • HAL Id : inria-00072969, version 1

Collections

Citation

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

Share

Metrics

Record views

138

Files downloads

199