BTA's don't move when they are provided what they like in terms of water quality, water flow and lighting. So, would a carpet move?-- not if it's content with the conditions being provided. Also, BTA's divide when under stress or when they grow large and do what comes natural. The fact your anemone was always moving makes me think it was stressed and dividing for that reason. In general, a carpet is going to require good water quality--and they are known to eat fish.