Great to know there are others out there with interest in blending local rocks with design. The attached link is a complete list of granites/ gneiss etc with all their aliases as well as their provenance. The picture of the rock you show is probably not a true schist (which would probably be more porous than you would like for a shower anyway). Look for the term 'migmatite' or 'gneiss' on this list. I found a few from the east coast of the US. The findstone website has lots more information on rocks too.

Here is a link that might be useful: MOST POPULAR GRANITES LIST

One thing I did when tiling our master bath was to take out a fair proportion of the onyx slices and replace them with slices I made of rocks our family found in Oregon. I am very happy I did it, even if it was labor intensive. I refitted most of the tiles back on the mesh with weldbond and then thinset it to the wall as usual. If you can't source enough of what you want locally, maybe you can at least intersperse native rocks with them. It is a somewhat informal look, with rocks of random shapes and not entirely the same depth. But then again the onyx slices were random to start with. Just another possibility.

Here is a link that might be useful: And I *still* haven't taken pics of the whole room :)