Walking Iris (Neomarica gracilis)

Walking iris is a stunning spring bloomer for warm climates.  The bright blue and white flowers are about 3 inches across.  

An entire bed of these iris will bloom on the same day and for only one day.  The spectacle is repeated every few days throughout the spring months.

After flowering, a new plant starts to form on the end of the flower stalk.

The weight of the developing plant causes the stalk to bend over and touch the ground, where the plantlet will take root. 

This is where the common name "Walking Iris" comes from.  The plants "walk" across the landscape (very slowly).  The long narrow leaves are arranged in a fan shape, typical of other members of the Iris family.  They are thin and droopy, giving mass plantings a soft billowy texture.  There is a related species with yellow flowers that has a more upright habit.
Neomarica will grow in mostly sun to full shade.  USDA Zones 8 to 11 (native to Central and South America).  The higher the zone you're in, the more shade you should give them.  Plants generally grow about 18" to 2 feet tall.  They make a nice evergreen groundcover under small trees where they'll get a little shade.