Mechanical instabilities in periodic porous elastic structures may lead to the formation of homogeneous patterns, opening avenues for a wide range of applications that are related to the geometry of the system. This study focuses on an elastomeric porous structure comprising a triangular array of circular holes, and shows that by controlling the loading direction, multiple pattern transformations can be induced by buckling. Interestingly, these different pattern transformations can be exploited to design materials with highly tunable properties. In particular, these results indicate that they can be effectively used to tune the propagation of elastic waves in phononic crystals, enhancing the tunability of the dynamic response of the system. Using a combination of finite element simulations and experiments, a proof-of-concept of the novel material is demonstrated. Since the proposed mechanism is induced by elastic instability, it is reversible, repeatable, and scale-independent, opening avenues for the design of highly tunable materials and devices over a wide range of length scales.