I found a site that has a large number of math generators that can be used to create fractal-type puzzles. (apologies if it’s already listed here. I searched and didn’t find a mention). I know that there is an Inkscape L-system generator that does much the same thing, but these seem a little easier to me and there are MANY other functions to explore.
There are MANY math generators. I don’t even begin to understand them, but several would seem to have direct GF possibilities. You’ll have to explore the different functions, but look for those that “draw” something. For example, here are examples of a Hilbert Curve and a Moore Curve.
The output is a PNG file, so not immediately useful. Using your favorite drawing program, trace into a vector file, make a few strategic “walls” within the curve to break it into pieces and then cut away.
There are many drawing functions that might not be puzzle options, but would make some impressive engravings.
Try the Peano Curve. There are some options that will make interesting variations that will make outstanding fractal-type puzzles.