The automatic synthesis of abstract textures is, to some extent, feasible. As evidenced by abstract art theoreticians, one can think of an abstract picture as a tree of elementary shapes interacting according to a short list of compositional laws such as occlusion, exclusion and bordering, and by rendering rules such as transparency, tessellation and color selection. Randomizing the shape generator and the composition and rendering laws yields an algorithm generating random abstract textures. We have designed a user-friendly online tool that implements this algorithm.