Vinca Vine

Source: http://www.aboutvines.com/vinca_vine.shtml
The vinca vine, often called a periwinkle flower, is used often as a grass substitute in lawn areas. The plant will only grow to three to six inches off the ground, but the trailing stems of the vinca vine can spread up to eighteen inches.
One thing to note about the vinca vine, however, is that it is extremely invasive. This means that the vine will easily spread throughout the garden quickly and can overwhelm other plants. Great care needs to be taken to ensure that the vinca vine does not take over the entire garden.