We present a reprogrammable matter system that changes shape in a controllable manner in real-time and on-demand. The system uses origami inspired fabrication for self-assembly and repeated self-reconfiguration. By writing a magnetic program onto a thin laminate and applying an external magnetic field, we control the sheet to self-fold. The magnetic program can be written at millimeter resolution over hundreds of programming cycles and folding steps. We demonstrate how the same sheet can fold and unfold into multiple shapes using a fully automated program-and-fold process. Finally, we demonstrate how electronic components can be incorporated to produce functional structures such as a foldable display. The system has advantages over existing programmable matter systems in its versatility and ability to support potentially any folding sequence.