It sounds like it might be Setcreasea. The leaves are brilliant purple and the flowers resemble spiderwort flowers, but pink. It kind of vines and kind of mounds. If this is what you have, it is iron tough. I once pulled some out put it in my compost pile for a YEAR, and it refused to die, so I put it back in the ground and it never missed a beat! (Not invasive in my experience.)

Or. . .by any chance, could it be Oxalis triangularis,
commonly called purple shamrock? Compare your plant to
the photo in this link:

Here is a link that might be useful: Easy To Grow Bulbs

Thanks, Donnabaskets for your try. With my poor description, you made a good guess. But Carl118 was right. It is Oxalis! I'm so delighted with this beautiful plant. It's just grown beautifully over the winter in my window, and I'm hoping it will just keep growing.

Thanks for your help!

b.