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  • Letter
  • Open Access

Moiré patterns of space-filling curves

Henning U. Voss1,2,* and Douglas J. Ballon2

  • 1Cornell MRI Facility, Cornell University, Ithaca, New York 14853, USA
  • 2Department of Radiology, Weill Cornell Medicine, New York, New York 10065, USA

  • *Contact author: hv28@cornell.edu
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Phys. Rev. Research 6, L032035 – Published 12 August, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L032035

Abstract

It is shown on the examples of Moore and Gosper curves that two spatially shifted or twisted, preasymptotic space-filling curves can produce large-scale superstructures akin to moiré patterns. To study physical phenomena emerging from these patterns, a geometrical coupling coefficient based on the Neumann integral is introduced. It is found that moiré 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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Phys. Rev. Research 6, L032035– Published 12 August, 2024
  • Received 25 March 2024
  • Accepted 13 June 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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