Magnetotransport in a density-tunable two-dimensional electron gas that is modulated with a strong, atomically precise superlattice potential of a 15 nm period is investigated. For low densities, the system shows typical two-dimensional behavior. In the regime of large densities, however, a quasi-one-dimensional state is entered, in which the cyclotron gaps vanish and the quantum Hall effect breaks down. Both regimes, and the transition between them, are theoretically described in the framework of a quantum-mechanical tight-binding model.