Advances in the creation of computational materials are transforming our thinking about relations between the physical and digital. In this paper we characterize this transformation as a "material turn" within the field of interaction design. Central to theorizing tangibility, we advocate supporting this turn by developing a vocabulary capable of articulating strategies for computational material design. By exploring the term texture, a material property signifying relations between surfaces, structures, and forms, we demonstrate how concepts spanning the physical and digital benefit interaction design. We ground texture in case study of the Icehotel, a spectacular frozen edifice. The site demonstrates how a mundane material can be re-imagined as precious and novel. By focusing on the texture of ice, designers craft its extension into the realm of computational materiality. Tracing this process of aligning the physical and digital via the material and social construction of textures speaks back to the broader field of interaction design. It demonstrates how the process of crafting alliances between new and old materials requires both taking seriously the materialities of both, and then organizing their relation in terms of commonalities rather than differences. The result is a way of speaking about computational materials through a more textured lens.