A friend just brought me this plant and it's a little wilted. She doesn't know if it's an annual or perennial (we're Zone 5 Ontario) because it seeds so prolifically. It flowers beginning in July, and goes until frost. It has a very small, fibrous root, and the stem looks almost bamboo-like.
I think it is Persicaria amplexicaulis. A perennial. I like mine. It spreads not so much by seed as by rooting. With just the one little piece, it'll be quite some time before you have a clump.
Probably Polygonum persicaria, a real spreader depending on where it is planted. For some, it is a pest. The leaves often have a little blotch, but not always. It might be another Polygonum -- it's a little hard to tell.
