There are some low growing plants that are woody at the base but have soft stems on top. Horticulturalists refer to them as subshrubs. Candytuft is a subshrub that we grow in our gardens because of the mass of white flowers they produce in late spring.
They like good drainage. Therefore, it's best to grow them on slopes and in rock gardens if there is moisture and full sun. There are both annual and perennial types. Iberis sempervirens is the perennial.
The genius name is Iberis because many of the species are natives of Spain. The common name, Candytuft, comes from the word Candia, which was the ancient name of Crete.
On the Mediterranean...
Candytuft grew profusely on the shores of the Mediterranean Sea, and it is a very adaptable plant. After our cold winters it can look untidy but it can safely be gently pruned back.
The lacy look of the pure white flowers makes it an ideal companion for late blooming tulips and other colorful late spring bloomers. Intersperse three or five candytufts among other low growers in a bed and you'll be pleased by their presence as it unifies the whole effect.