Aggregate and fractal tessellations |
| |
| Authors: | Konstantin Tchoumatchenko Sergei Zuyev |
| |
| Institution: | (1) France Telecom R&D, 38-40 rue du Général Leclerc, 92794 Issy-Moulineaux, France. e-mail: Konstantin.Tchoumatchenko@rd.francetelecom.com, FR;(2) Statistics and Modelling Science Department, University of Strathclyde, 26 Richmond str., Glasgow, G1 1XH, UK. e-mail: sergei@stams.strath.ac.uk, GB |
| |
| Abstract: | Consider a sequence of stationary tessellations {Θ
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 Θ1 whose nuclei lie in C
0(x
i
0). An aggregate tessellation Θ0
n
consists of the aggregate cells of level n, C
0
n
(x
i
0), defined recursively by merging those cells of Θ
n
whose nuclei lie in C
n
−1(x
i
0).
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 {Θ
n
}.
Received: 3 June 1999 / Revised version: 22 November 2000 / Published online: 24 July 2001 |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
