Meg Mitchell wrote: OP mentioned planting purple potatoes intentionally, and I'm not sure how else they can spread besides if you moved some dirt around.
OP also said "no matter what I plant I always get purple potatoes" which sounded like they were planting one thing and getting another.
I move my potatoes round on a four-year cycle, and I always get some volunteers the next year - some are from tiny weeny little tubers but others are like "doh - how did I miss THAT one?". I suspect that although I try and rigorously remove the volunteers, some escape my notice long enough to build up a new tiny tuber which then comes up again the next year. Another possible source of potatoes in the wrong place, especially if they are on the surface, would be if you've added peelings to your
compost and they've not been killed by the composting process and have sprouted from those.