TL;DR
This paper computes the Assouad and conformal Assouad dimensions of specific classes of self-affine carpets, extending understanding of their geometric complexity and scaling properties.
Contribution
It provides explicit calculations of the Assouad and conformal Assouad dimensions for Bedford-McMullen and Lalley-Gatzouras carpets, including non-self-similar cases.
Findings
Assouad dimension of Bedford-McMullen carpets determined
Assouad dimension of Lalley-Gatzouras carpets determined
Conformal Assouad dimension computed for non-self-similar carpets
Abstract
We calculate the Assouad dimension of the self-affine carpets of Bedford and McMullen, and of Lalley and Gatzouras. We also calculate the conformal Assouad dimension of those carpets that are not self-similar.
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