Mimosa pudica is another fast-moving plant, which isn't carnivorous (and not closely related) Some Drosera (sundew) species actively curl their leaves around p

Mimosa pudica is another fast-moving plant, which isn't carnivorous (and not closely related) Some Drosera (sundew) species actively curl their leaves around prey, but rely on the prey being stuck to their leaves already, so different to the mechanism of a VFT. Drosera and VFT are in the same family, so are pretty closely related. There's Utricularia (bladderworts) which are capable of catching prey rapidly, but the plant itself doesn't really move I guess.