Tradescantia virginiana, or spiderwort. It is a seedling a friend if mine gave me. It is a deep blue- violet. I love this one. Some I have seen are rather pale. I used to have quite a few different colors, but when I cut the garden waaaaayyyyy back this was the only one I kept. I have it in a couple places just in case something happens to one of them, since it is a seedling. Spiderworts tend to "travel" but this one is quite well behaved. It is happy to stay put.
