WHEN DOES A BEDFORD–MCMULLEN CARPET HAVE EQUAL HAUSDORFF AND TOPOLOGICAL HAUSDORFF DIMENSIONS?

Huo-Jun Ruan () and Jian-Ci Xiao
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Huo-Jun Ruan: School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, P. R. China
Jian-Ci Xiao: School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-9

Abstract: In this paper, we provide a complete characterization on when the Hausdorff and topological Hausdorff dimension of a given Bedford–McMullen carpet coincide. These two dimensions have a common value if and only if the carpet is either the Cartesian product of [0, 1] and a self-similar set, or it is one of the two diagonals of the unit square.

Keywords: Hausdorff Dimension; Topological Hausdorff Dimension; Bedford–McMullen Carpet (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21501942

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DOI: 10.1142/S0218348X21501942

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