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Fractal n-hedral tilings of ℝd

Part of: Designs and configurations Classical measure theory Discrete geometry

Published online by Cambridge University Press:  09 April 2009

You Xu
You Xu
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA e-mail: yoxst+@pitt.edu
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Abstract

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An n-hedral tiling of ℝd is a tiling with each tile congruent to one of the n distinct sets. In this paper, we use the iterated function systems (IFS) to generate n-hedral tilings of ℝd. Each tile in the tiling is similar to the attractor of the IFS. These tiles are fractals and their boundaries have the Hausdorff dimension less than d. Our results generalize a result of Bandt.

Keywords

Tilingfractalself-similar setiterated function system

MSC classification

Secondary: 52C22: Tilings in $n$ dimensions 28A80: Fractals 05B45: Tessellation and tiling problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 3 , June 1999 , pp. 403 - 417
Copyright
Copyright © Australian Mathematical Society 1999

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