For periodic/symmetric tilings, it seems somewhat "obvious" to me that it just comes down to working out the right group of symmetries for each of the relevant shapes/tiles, but its not clear to me if that carries over in any nice algebraic way for more complicated objects such as a penrose tiling and just following wikipedia just leads to the statement that groupoids come into play, but with no references to example constructions! Moreover, at least naively thinking about, it seems any such algebraic approach should naturally also apply to fractals.

- what references am I somehow not able to find that do a good job talking about this further?
- is my "intuition" that the mathematical structure for at least some classes of fractals and quasicrystals being equivalent correct?