White/purple mineral , i think is amethyst
Looks more like feldspar - can you please post some more photos?
Also, where is whitefish?
Whitefish Bay in Michigan where the Edmund Fitzgerald sank.. Fist-sized rock. White and purple crystals. Found on beach Whitefish Bay . More pictures soon
Google amethyst uncut or rough and you will see it for yourself.
I used google again and google came up with this document;
I think you have an agate there.
Amethyst has white crystals as well as purple. That is what lead to my conclusion.
From the later pictures you posted, it looks like a pebble of waterworn quartz in either sandstone or basalt matrix. The host rock of the lake superior agates is volcanic basalt, and that is the most likely combination.