Hausdorff dimension of the limit sets of some planar geometric constructions
type: Item
instance of: scholarly article
title: Hausdorff dimension of the limit sets of some planar geometric constructions
zbMATH Open document ID: 1116.28008
author: Krzysztof Barański
published in: Advances in Mathematics
publication date: 2007-03-09T00:00:00Z
review text: This interesting paper concerns the Hausdorff and box dimensions of the limit sets for various geometric constructions in the plane. In the introduction, the author gives a comprehensive survey of results known for extensions of the class of selfsimilar sets, in particular for Moran constructions and (more general) Moran-like constructions. For a Moran-like construction the Hausdorff dimension and the box dimension of the limit set coincide. He also gives a survey of results known for some special non-Moran-like constructions for which these two fractal dimensions can be computed rigorously. In particular, in 1984, Bedford and McMullen computed independently these dimensions for some self-affine limit sets known as the generalized Sierpiński carpets. The author's new results concern a general class of non-Moran-like planar geometric constructions, called the rectangle-like constructions. This class is essentially larger than that with self-affine limit sets. In particular, he computed the Hausdorff and the box dimension of the flexed Sierpiński gasket defined by Rudnik in 1989.
reviewed by: Maria Moszyńska
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 5132554
zbMATH Keywords: fractals
zbMATH Keywords: Bedford-McMullen carpets
MaRDI profile type: Publication
full work available at URL: j.aim.2006.06.005
OpenAlex ID: W1971471503
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DOI: 10.1016/J.AIM.2006.06.005
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description: scientific article; zbMATH DE number 5132554