Hi Judianni, Welcome to All Things Plants!
Dichondra carolinensis spreads by stolons/runners and here in Florida it seems to spread fairly quickly. Many people consider it a weed while many others think it makes a lovely ground cover. Foot traffic doesn't seem to bother it as far as I know; we had it growing amidst the lawn in the backyard at our old house and it was mowed and walked on a lot without any problems. It seemed to prefer moist soil so I'm not sure how it would do in areas of the country that experience long periods of low rainfall and drought.
Lin
