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When Does A Bedford–Mcmullen Carpet Have Equal Hausdorff And Topological Hausdorff Dimensions?

Author

Listed:
  • 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)

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.

Suggested Citation

  • Huo-Jun Ruan & Jian-Ci Xiao, 2021. "When Does A Bedford–Mcmullen Carpet Have Equal Hausdorff And Topological Hausdorff Dimensions?," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-9, November.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21501942
    DOI: 10.1142/S0218348X21501942
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