We bought a house last year and this is one of the few plants that came with it that I don't know...
Setcreasea pallida, a wandering jew relative that is sometimes called "purple heart". Not hardy in the north but will winter over in the south.
It's nice in a hanging basket, indoors or out, and its pink flowers look great with the purple thinginess! You've already found out how easy it is to take cuttings from.
My mom had a some pieces fall out of a basket and now she has a bed full of it. She doesn't mind one bit since she could never get anything to grow in that spot and pretty purple grassy thingies are a big improvement over bare dirt :)
It's good to know it grows well...my hubby accidentally chopped up the other patch of it to make room for some other plants he bought!
When do the pink flowers show up? I haven't seen them!
usually by mid to late summer. they are pretty small though and are not particularly showy but they do add a bit of interest.