Spiderwort (Tradescantia), fam. Commelinaceae.
Virginia Spiderwort (Tradescantia virginiana) is grown in the garden beds of the city. It is easily distinguished from most other plants by its three-petal flowers, which do not fade in the end of the day, but, on the contrary, transform into semiliquid substance. Another plant, Wandering Jew (Setcreasea purpurea = Tradescantia pallida), behaves similarly; it is usually grown indoors, shown in the last photo.
The leaves may be used to heal wounds (like those of plantain). They are edible, though rather acrid; domestic pets often eat them, craving for vitamins. They are also used against diabetes, flatulence, and tuberculosis.