We explore how to bring physical affordance to mobile touch devices. We present Rock-Paper-Fibers, a device that is functionally equivalent to a touchpad, yet that users can reshape so as to best match the interaction at hand. For efficiency, users interact bimanually: one hand reshapes the device and the other hand operates the resulting widget. We present a prototype that achieves deformability using a bundle of optical fibers, demonstrate an audio player and a simple video game each featuring multiple widgets. We demonstrate how to support applications that require responsiveness by adding mechanical wedges and clamps.