That's why we use binomials. Excerpt from Wikipedia... Vinca minor (common names lesser periwinkle or dwarf periwinkle) is a species of flowering plant native to central and southern Europe, from Portugal and France north to the Netherlands and the Baltic States, east to the Caucasus, and also southwestern Asia in Turkey. Other vernacular names used in cultivation include small periwinkle, common periwinkle, and sometimes in the United States, myrtle or creeping myrtle,[1] although this is misleading, as the name myrtle normally refers to the Myrtus species.

I can't make out the leaves on your plant, but it looks like maybe Callirhoe involucrata.

Periwinkle (Vinca minor) was the first thing that popped into my mind, too, but I have to say that its flowers are usually blue, not purple. It's a staple of my parents' house near Philadelphia because my mother just loves it. I think it's pretty, too, although I don't grow it where I live now. I understand it has the potential to be invasive, although in my experience it's usually mostly "persistent", rather than "invasive" (unlike English ivy, or Lamium, or Bishop's weed).

Here is a closer Look. It's not Alchemilla or Potentilla. This is a low ground cover with leaves about 1 inch wide that have serrated white edges. Growing in Vancouver BC.