The center of a Venus Flytrap's rosette tends to move to one side as successive leaves bury themselves a little deeper into the soil and new leaves emerge from the tissue at the base of these new leaves. Leaves generally stop growing from the oldest tissue underground, the base of the dead leaves that formed the old rosette, unless a new small division and new growing rosette begins to form from some of the older rhizome tissue, in which case the Venus Flytrap will have two or more growing crowns, the center of each of which will continue to move as newer, larger, deeper leaves develop to one side of the rosette.
In addition, the center of the growing rosette is offset by a flowerstalk when the plant blooms. The flowerstalk is the terminal growth of the rosette of a mature Venus Flytrap, and after it is produced, and typically after a stall in growth of several weeks, a completely new growing rosette begins to grow to one side of the stalk or plant, and as it produces successive leaves, its growing rosette will also move, perhaps up to a couple inches or more if it is a mature plant, before it produces its own flowerstalk the next season.
At some point, the rhizome tissue that connects the various new growing rosettes (the various divisions) dies, leaving individual plants in a clump that all originated from a single parent plant.
Yes, Venus Flytraps can and do move sideways. Sometimes those in pots, which were carefully centered or placed when planted, end up at the side of the pot pressing against the edges before one transplants and carefully recenters the plant again.
