Without becoming invasive, common alyssum, Lobularia maritima, can almost naturalize in favorable situations. It disperses seed profusely, so often appears where it is an asset to the garden. Since it is so docile, it subordinates to more vigorous plants that it mingles with. It does well on loosely set stone walls. If necessary, it is easy to remove or relocate.
Common alyssum blooms with tiny but profuse white flowers. If they naturalize, varieties with pink or purple bloom eventually revert to white bloom after a few generations. Some varieties revert slower than others. Although popular as a warm season annual, alyssum can continue to bloom through next winter. Individual plants may survive for a few years.
Mature alyssum plants might get a bit higher than half a foot, but will get no higher than a foot. If they perform for more than a year, their progeny may begin to replace them before they get shabby. After removal, shabby plants, with a bit of shaking over bare spots, may share their last seed. Alyssum grows easily from seed, and is available in cell packs too.