I did manage to track down this one though. It's called "saxifraga" and there are many varieties. The ones I prefer are notable for their 5 asymmetrical petals. I love these plants. They are whimsical and charming, and yet tough enough to survive the Osaka summers. (They don't really like the heat though.)
Here are the two latest saxifraga additions to my garden.
May they live long and prosper! (^.~)/