Weakly separated self-affine carpets
Bal\'azs B\'ar\'any, Levente David

TL;DR
This paper investigates the Hausdorff and box-counting dimensions of weakly separated self-affine carpets, establishing formulas and limits that generalize previous results for these fractal sets.
Contribution
It provides new formulas and limits for the Hausdorff and box-counting dimensions of weakly separated self-affine carpets, extending existing dimension theory.
Findings
Hausdorff dimension equals the limit of the Baránski formula.
Box-counting dimension is the limit of the Feng-Wang formula over iterated IFS.
Derived explicit dimension values for specific examples.
Abstract
In this paper, we study the Hausdorff and the box-counting dimensions of diagonally aligned self-affine carpets whose projections to the - and -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 -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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