Liriope spicata

Good vigorous spreading groundcover that can be used as a low maintenance substitute for turfgrass in small spaces. Grows 8–12 inches tall and prefers full sun to very light shade. Drought tolerant. Small light blue flowers in late summer followed by black, bead-like fruit.
Evergreen foliage. Space 8–12 inches apart. Perennial. Hardy in Zone 4.