In The Garden: Need some help identifying my husbands favorite plant

I bought this succulent a couple of years ago and it had no ID tag. Does anyone recognize this plant? I thought it might be a sedum spurium but most of the information I've found on this type of plant indicates that it flowers. The plant that I have has never flowered.

My husband LOVES this plant and I need to get a few more to put around our ponds.

Thanks!

 

In the very top left of your pic there seems to be a flower. Is it growing through your mystery plant..or from it? Any chance of a close up?

 

I'm ashamed to say that that is a weed growing through my plant.

Attached is a close up picture of the mystery purple plant.

Thanks

 

Looks like Commelinaceae... Callisia repens?

 

Thank you Lila! I researched that plant name and that's exactly what it is. The mystery is solved!