  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.
