Smoke Likes Her Stone

Our kitten, Smoke, has a few odd quirks, as I'm sure most kittens and
cats do. However, this one is truly weird. We have a flat stone,
which we picked up on the shore of Lake Ontario. Smoke goes over to
the stone and either rests her front paws on it, sits on it as though
she's trying to hatch it, or just cozies up next to it. She will race
into the room and go right for the stone. A touchstone? Who knows?

Does anyone have any insight into this weird behavior, or have stories
of similar weirdness?