A little more information please. How much water will this area get? I have a area covered by white clover (invasive and yes it does grow in Tucson) that my desert tortoise loves. It gets regular watering along with the grass. I have tried herbs but have had no luck in the full sun. Mint does very good in full sun and the tortoise doesnt like it. Its just a little to invasive for my taste but fills in areas quickly.

Common Periwinkle, Myrtle, or Vinca Vinca minor Periwinkle or myrtle is an excellent, evergreen ground cover with dark-green foliage and purple, blue, or white flowers, depending on the variety. It blooms in April and sometimes again in the fall. The plant grows about 6 inches tall, spreading in all directions by sending out long, trailing and rooting shoots that make new plants. It is best in shade, but will grow satisfactorily in full sun. The foliage color is richer in partial shade, but more flowers are produced in the sun. This ground cover is most commonly used for underplanting trees and shrubs, on shaded slopes, or [b]on the north side of buildings[/b]. Rooted cuttings or established plants are normally spaced from 12 to 18 inches apart. At a 6-inch spacing, a complete cover will be produced in one year. Plant in the spring in areas with severe winters. Spring-flowering bulbs interplanted with periwinkle will lend color and interest to the ground cover planting. Daffodils are particularly well suited to this since they bloom at the same time as periwinkle and do not require frequent division.

Depending how low. Potentilla fruticosa is native to bogs. K. Dykes gets up to 24" and cascades. Of course it is deciduous but has yellow blooms all summer.

OK I think I got a good picture. I had to dig it out of the snow!!!! The leaves are really tiny. Pic looks a little dark here. I'll try with a flash next.