Here in Texas it is a low (8-12") thatch of a ground cover. People can plant it in the shade or sun, and usually take the weedeater to the edge to keep it from creeping into the lawn.

It's in the foreground and around the crape myrtle in this photo.

It doesn't have any flowers that I know of. Well, you know how that goes--it probably does, but nothing that is ever conspicuous.

How big do you want your ground cover? Rosemary is quite a hedge around here, and it does a fine job of covering the ground. Or something little, like oregano. That is a pretty ground cover here also.

SRS