There are no fancy varieties, but many different fancy names for knotweed. It used to be known as Polygonum capitatum, but is now easier to research as Persicaria capitata. The many common names include pink knotweed, pink clover, pink fleece flower, pinkhead, pink bubbleweed and smartweed. Obviously, the tiny and spherical blooms are pink, about the color of bubble gum. Each small leaf has a distinctive brown chevron, which makes the collective foliage rather bronzy. The wiry stems can not stand much more than three inches high, but creep indefinitely, rooting as they go. Knotweed is an excellent but potentially invasive groundcover, and is also a nice component to mixed plantings in large urns or behind retaining walls, where it can cascade several inches over the edges. A bit of partial shade is no problem. Bloom continues through the end of summer, and resumes at the end of winter.
Tony Tomeo 
Very interesting. I’ve never seen this one. We have a couple of native Persicaria species, like P. pensylvanica. They’re branching, but the individual flowers look like these.
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This was more popular years ago. I still see it where it is naturalized in abandoned or less refined gardens, but have not seen it in a nursery in a very long time. I got a six pack of it in the early 1990s.
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Here, we call it Mexican Knotweed. I found anything that contains the name Mexican or weed will grow extremely well in my garden and it did. This little plant accidentally came with me when I moved 20 years ago and it is still creeping around the garden.
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That is how it typically works. I know of no one else who planted it intentionally. It just lingers from what was planted decades ago. I planed mine in the early 1990s, but it did not last. I eliminated it before it escaped into neighboring gardens.
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. . . but this one should not be Mexican. It is Asian. We learned it as Japanese.
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I think it has to do with where I live and marketing.
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Ah, like the African flame bush from New Zealand . . . with purple flowers.
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We have Fallopia japonica (syn. Polygonum cuspidatum) here, which we call Japanese knotweed. It’s a big problem. Your type looks more decorative.
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It is, but it can also be invasive. I do not find it to be aggressively so, but it concerned me enough to get rid of mine before it got into neighbor’s gardens.
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