Random textures differ from natural textures because they lack structure. Structure is a concept that is difficult to formalize, however, we generally observe that it is associated to spatial dependency between adjacent pixels. Random textures, in fact, are characterized by independent pixels, while natural textures show some local dependencies. In this paper, we propose a measure for this local dependency. We find the minimal distance between pixels that ensures spatial independence. We assume that this distance can be used to help modeling textures, to set the size of operating windows in texture synthesis algorithms, and to compute a simple indicator of texture scale.