Plants from the genus Persicaria (syn. Polygonum) have some weed potential - indeed, the common name for the plants is 'knotweed'! However, some of them have interesting and often alluring foliage, including, Persicaria virginiana (sometimes called P. filiformis, which may indeed be the more correct name; it was previously known as Tovara virginiana). It comes from the Himalayas, Japan and the east of North America. In my garden, it is herbaceous, dying right back to the ground in winter and re-emerging in spring with rich green leaves with distinctive purplish-brown bands. It can apparently grow taller than 1 metre; mine gets to about 80 cm in height. It grows best in reasonable soil, in a position sheltered from hot afternoon sun and strong winds. I usually support my plant with cradle stakes during summer. If a plant with leaves or flowers of a similar colour to the leaf bands can be grown nearby as an echo, it can be a thrilling combination. Some ideas are dark-leaved Begonia, Iresine herbstii 'Wallisii' or Alternanthera dentata. The down side of this Persicaria is its self-seeding habit. I once foolishly left the flower-spikes on the plant, thinking that the slim wands of tiny red blooms were rather pretty - in spring, I had literally thousands of baby plants come up through the lawn and garden bed. So the flower-stalks need to be cut off as soon as you notice them.
This species has a few cultivars, one being called 'Painter's Palette'. It is a rather gaudy plant with variegated leaves - a central V-shaped brown mark, yellow patches and reddish tints. It sounds rather horrid but placed in a tropical-style border with hot-coloured Dahlia, Salvia or Alstroemeria and given the contrast of some nearby dark foliage, it can look wonderfully flamboyant. This one has self-seeded in my garden too, so again I need to be more vigilant about cutting off the flower-stalks when they first appear.
Persicara belong to the family Polygonaceae.