I’m a retired engineer (PhD Princeton University, 1968, Aerospace Engineering) with about 50 years of experience in mathematical modeling. Naturally, when I retired a few years ago, I undertook recreational mathematics. I have experience in plane curves and spirals, tessellations, fractal tiling, fractals, and Archimedes 'The Method.'
I have many posts at the National Curve Bank on these subjects as well as a few pages of mathematical art and animations at Pinterest: (1) Tessellations, Fractal tiling, & more, (2) Fractals, and (3) A new paradigm for fractals.
My chop, or seal, on the left is an original fractal tiling. The tiles decrease in size in such a way that it is self-similar at all scales. In principle, you can fill any shape with any other shape(s) to any number of tiles with fractal tiling. This image has 5000 tiles. There are many examples at the Pinterest page noted above.