We present a novel apparatus for generating internal waves of arbitrary size and shape, including both phase-locked and propagating waves. It is an actively driven, flexible “magic carpet” in the base of a tank. Our wave maker is computer-controlled to enable easy configuration. The actuation of a smooth, flexible surface produces clean waveforms with a predictable spectrum, for which we derive a theoretical model. We demonstrate the versatility of our wave maker through an experimental study of linear and nonlinear, isolated, and combined internal waves, including some that are sufficiently nonlinear to break remote from their source.