Herniaria glabra is known as Green Carpet in the landscaping business, because of its ability to spread and cover. One plant can easily spread out to 2 feet. Because Herniaria has a tap root, it is extremely drought tolerant.
Many people never notice it flowering because the white blossoms are so tiny and have no petals. But the foliage remains attractive, turning a bronzy red in winter. It's great in heavy foot traffic areas because without flowers, it doesn't attract bees.