ON THE PATIOThe native Silver ponyfoot, sometimes called Silver ponys foot, is
Dichondra argentea according to the Wildflower Center, but the plants at nurseries are frequently labeled 'Silver Falls'. Mine started out as the "Spiller" in a basket hanging near the wall at right about 3 years ago.

Some strands landed in the granite below, rooting and gradually spreading. Last spring the ponyfoot trotted across the sidewalk to the decomposed granite area next to the patio and it kept going. Even in Austin's fairly mild zone 8 winter, this groundcover gets frozen back, but there are usually enough rooted knobs still alive to get it restarted.

Now it's gently lapping the rocks around the fountain.
IN THE FRONT
Near the steps to the veranda a bowl of Silver Pony foot dripped down and has likewise spread to fill this area of decomposed granite. It will look better once the oleander leaves are removed!
Pam/Digging shows Silver Ponyfoot
on a garden tour, used to fill in the spaces and soften an area of large flat stones.