This groundcover, and I hope that's not too generous a term for this, is growing at an apartment building a few blocks from me, one that has other interesting plants - that, and now nicely these are filled in, make me think this was deliberately planted. I started a thread on flowers growing in the fall, so I've been trying to pay attention. This is covered with what I thought were individual flowers, but now I see that what I thought were single flowers are little round clusters of around six, standing up on thin purple pedicels (peduncles??), often in pairs, and some of these stems are sparsely haired. The flower stems seem to emerge from the base of the leaves. The white flowers have five petals, blue anthers and something is yellow in the centre. The deltoid-shaped leaves, alternately arranged on thin purple stems, have entire margins. I can see hairy leaf edges that in some cases appear rimmed in purple - I didn't notice that at the time and didn't look to see what the underside of the leaves look like - purple and hairy? Not one leaf is turned over. I'll have to go check.
Try Persicaria sp...there are lots.... in Polygonaceae Often used to be called Polygonum. Persicaria - Wikipedia Maybe..... Persicaria (syn Polygonum) microcephalum var. sphærocephalum. red dragon knotweed. You can see the red blotches on your leaves. Polygonum microcephalum var. sphærocephalum - Google Search 'Red Dragon' Knotweed flower close-up; photo by ALJ - Google Search excellent images on this link... Plant of the Month Quote above...blinking name changes... "Kunming Knotweed; Polygonum microcephalum var. sphærocephalum (Wall. ex Meisn.) H. Hara 1971 'Kunming' = Polygonum sphærocephalum Wall. ex Meisn. 1832 = Polygonum Thunbergii hort., non S. & Z. 1846 'Langthorn's Variety' = Persicaria sphærocephala (Wall. ex Meisn.) H. Gross. 1913 = Persicaria alata hort., non (Buch.-Ham. ex D. Don) Nakai1914 = Persicaria nepalensis hort., non (Meisn.) H. Gross 1913 = Persicaria sp. Kunming hort. POLYGONACEÆ; Knotweed Family" Found in Vancouver.... Silver Dragon Fleeceflower (Persicaria microcephala 'Silver Dragon') in Vancouver Victoria Burnaby Penticton Coquitlam British Columbia BC at GardenWorks Quote above......"Silver Dragon Fleeceflower is an herbaceous perennial with a ground-hugging habit of growth."
Thanks, Silver surfer. I'd looked up Fallopia, didn't think to move on to Polygonum or Persicaria. That's what those flowers reminded me of! I was going to say that the leaf markings seem a little more like some I'm seeing as Persicaria nepalensis (or nepalense), but then I got to the bottom of your synonym list (!), and I have found Arthur Lee Jacobson's article at Plant of the Month where he writes of Polygonum microcephalum var. sphærocephalum being offered as P. nepalensis. Actually, he has a lot to say about this. I think we have a winner, but not 'Silver Dragon'.