In this paper we introduce a new technique to texture surfaces. Our approach has the advantage that the texture does not have to be computed at each point of the surface. Rather, we precompute a small set of texture maps which we then map aperiodically onto the surface. The algorithm borrows from recent mathematical results in the area of aperiodic tilings of the plane. To demonstrate the feasibility of the method we apply it to the rendering of water surfaces and caustics.