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New Classes of Random Tessellations Arising from Iterative Division of Cells

Part of: Geometric probability and stochastic geometry Stochastic processes Designs and configurations

Published online by Cambridge University Press:  01 July 2016

Richard Cowan
Richard Cowan*
Affiliation:
University of Sydney
*
∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email address: rcowan@mail.usyd.edu.au
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Abstract

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We present new ideas about the type of random tessellation which evolves through successive division of its cells. These ideas are developed in an intuitive way, with many pictures and only a modicum of mathematical formalism–so that the wide application of the ideas is clearly apparent to all readers. A vast number of new tessellation models, with known probability distribution for the volume of the typical cell, follow from the concepts in this paper. There are other interesting models for which results are not presented (or presented only through simulation methods), but these models have illustrative value. A large agenda of further research is opened up by the ideas in this paper.

Keywords

Random geometrytessellationiterative divisionfractalshape distribution

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 05B45: Tessellation and tiling problems
Secondary: 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 42 , Issue 1 , March 2010 , pp. 26 - 47
Copyright
Copyright © Applied Probability Trust 2010 

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