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arXiv · 2506.06851

Weakly separated self-affine carpets

Balázs Bárány·Levente David
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Abstract

In this paper, we study the Hausdorff and the box-counting dimensions of diagonally aligned self-affine carpets whose projections to the $x$- and $y$-axes satisfy the weak separation condition. In particular, we show that the Hausdorff dimension equals the limit of the Bara\'nski formula, and that the box-counting dimension is the limit of the Feng-Wang formula taken over the $n$-fold compositions of the IFS. We also prove several equivalent formulas for the box-counting dimension, and derive the dimension values for two examples.

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Balázs Bárány, Levente David. 2025-06-07. Weakly separated self-affine carpets. https://arxiv.org/abs/2506.06851

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