Year: 2026
Type: preprint
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 $\overline{\dim}_{\mathrm B}(\mathcal S_θ)\le 2\dim_{\mathrm H}(S)-2$. Finally, we conjecture that both dimensions equal this bound at every non-resonant angle. Sections 2 and 3 are formalised in Lean.
Source: arXiv (Cornell University)
Author: Neroli, Ziyu
Institution: Imperial College London
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214379729