Another possibility might be Sedum sieboldii -- there are numerous cultivars. [purple's renamed one was formerly known as Sedum spurium 'Purpurteppich'.]

I've had it since June in a container and it's had many buds but I've never seen it bloom. I've put it in my garden now we will see what happens. I agree it is comparable to the one you mentioned.

I kind of doubt that is C. tetragona. It looks much too dense and lush, and most of the stems have too much floppiness to them. It is tough to be sure though since I don't really know what this plant does if it is extremely etiolated. Also, the "points" of each leaf look rather soft on Love's plant, whereas C. tetragona has distinct, very slightly woody leaf tip that are pretty sharp. Worse, I can't propose an alternative. I would suspect something more like a Sedum than a Crassula though...

My neighbor gave me one of those, he called it ice plant. It stays outside all winter in a pot, and also under the trees, it blooms in june here, and is easy to make cuttings that take quite easily. Darlene