<sub>I am encouraged to give this answer by the comment of the OP "My interest is in creative, non-digital ways of experimenting with mathematical theories, especially aiming for publication".</sub>

My colleague Hendrik Lenstra used his expertise with elliptic curves to fill in the empty hole at the center of a litho by Escher, see <A HREF="https://escherdroste.math.leidenuniv.nl/notices_desmit-lenstra.pdf">Artful Mathematics</A>:

<IMG SRC="https://i.sstatic.net/gWmFu.jpg" WIDTH="300"/>
<IMG SRC="https://ilorentz.org/beenakker/MO/Escher_Lenstra.gif"/>

*Original litho on the left, zoom into the completed hole at the right.*

> We shall see that the lithograph can be viewed as drawn on a certain
> elliptic curve over the field of complex numbers and deduce that an
> idealized version of the picture repeats itself in the middle. More
> precisely, it contains a copy of itself, rotated clockwise by
> $157.6255960832\ldots$ degrees and scaled down by a factor of $22.5836845286\ldots$