PreprintCC BY 4.0arXiv
Moiré Pattern of Rotated Sierpiński Gaskets
Abstract
We study the moiré pattern formed by the intersection of a planar Sierpiński gasket and a copy rotated about its centre. At every resonant angle, we prove that the intersection is of finite type and compute its Hausdorff and Minkowski dimensions from an explicit finite matrix; for Lebesgue-almost every angle, we bound its upper Minkowski dimension by dim̅B(𝒮θ)≤ 2dimH(S)−2. Finally, we conjecture that both dimensions equal this bound at every non-resonant angle. Sections 2 and 3 are formalised in Lean.
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BibTeX
@misc{neroli2026moiré,
title = {{Moiré Pattern of Rotated Sierpiński Gaskets}},
author = {Ziyu Neroli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30235},
eprint = {2609.30235},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30235},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Moiré Pattern of Rotated Sierpiński Gaskets
AU - Ziyu Neroli
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30235
UR - https://arxiv.org/abs/2609.30235
AB - We study the moiré pattern formed by the intersection of a planar Sierpiński gasket and a copy rotated about its centre. At every resonant angle, we prove that the intersection is of finite type and compute its Hausdorff and Minkowski dimensions from an explicit finite matrix; for Lebesgue-almost every angle, we bound its upper Minkowski dimension by dim̅_B(𝒮_θ)≤ 2dim_H(S)−2. Finally, we conjecture that both dimensions equal this bound at every non-resonant angle. Sections 2 and 3 are formalised in Lean.
ER -