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arXiv · 2403.16891

Moir\'e patterns of space-filling curves

Henning U. Voss·Douglas J. Ballon
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Abstract

It is shown on the examples of Moore and Gosper curves that two spatially shifted or twisted, pre-asymptotic space-filling curves can produce large-scale superstructures akin to moir\'e patterns. To study physical phenomena emerging from these patterns, a geometrical coupling coefficient based on the Neumann integral is introduced. It is found that moir\'e patterns appear most defined at the peaks of those coefficients. A physical interpretation of these coefficients as a measure for inductive coupling between radiofrequency resonators leads to a design principle for strongly overlapping resonators with vanishing mutual inductance, which might be interesting for applications in MRI. These findings are demonstrated in graphical, numerical, and physical experiments.

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Henning U. Voss, Douglas J. Ballon. 2024-03-25. Moir\'e patterns of space-filling curves. https://doi.org/10.1103/physrevresearch.6.l032035

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