We introduce a Lamb-wave medium with tunable propagation velocities, which are controlled by a two-dimensional heating pattern produced by a laser beam. We utilized it to demonstrate that waves in an appropriately designed medium can propagate in the form of concentric squares, in contrast to the circular patterns typically emitted by a point source in a homogeneous two-dimensional medium. In order to avoid the concentration of wave energy in the middle of the sides of the squares, we propose two alternatives: a square wave that either rotates or exponentially decelerates as it expands. Additionally, we present how circular waves can be transformed into spiral waves utilizing the same tunable medium. The described experimental platform offers a new tool to generate shaped pulses for ultrasonic applications, which has the potential to improve the efficiency of energy and information transport.