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".

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 Artful Mathematics:

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 $22.5836845286\ldots$

_{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".}

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 Artful Mathematics:

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 $22.5836845286\ldots$

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".

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 Artful Mathematics:

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 $22.5836845286\ldots$

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".

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 Artful Mathematics:

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 $22.5836845286\ldots$