Looks like creeping phlox, but apparently is Trailing Rosemary? One pinner said: Trailing Rosemary produces beautiful blue foliage. It requires little water, and has a moderate growth rate. It has no allergens, but yet is very fragrant.
Best sun tolerant plants: Silver falls dichondra shimmers and cascades. This trailing plant is a silvery blue-green. It’s hard to believe that something so enchanting could be heat- and drought-tolerant!
Trailing Bellflowers—Attracts Butterflies This drought-resistant ground cover is populated with beautiful lilacblue star-shaped flowers. Let it cascade down walls, hang from a planter or fill your rock garden. It will grow in almost any soil.