I don't know how weird this is, because I didn't have cats growing up, but I have four cats now, and they all follow me from room to room. It's not like ducklings in a line, but once I move rooms, I just have to wait a few minutes, and then they'll all show up, one after another, trying to look bored and unconcerned, like "Oh, hey Mom, didn't know you were here. I just wanted to be in here all of a sudden."
Except Falstaff, who follows me from room to room, crying "MAMA" at the top of his little kitty voice.