Koenigia islandica; The Iceland-purslane is a small annual plant on Iceland. It grows in areas with sparse vegetation. In the highlands I noticed this plant is often grows in hollows around stones created by wind or water action around the stone. Apparently the hollow around the stone gives the necessary protection. I habve seen the species also in the lowlands, even in mud banks in estuary's close to the sea. Characteristic are the red stems, the glossy green little leaves and the minute flowers. The photo of "flower detail"may suggest it has a tubular flower shape. That is not so: the petals are free, only joined at the base. Note that sepals are lacking.
It is a member of the dock family (Polygonaceae). The Icelandic name of this species is Naflagras.