Texturing using a set of two dimensional image maps is an established and widespread practice. However, it has many limitations. Parameterizing a model in texture space can be very difficult, particularly with representations such as implicit surfaces, subdivision surfaces, and very dense or detailed polygonal meshes. This paper proposes the use of a new kind of texture based on an octree, which needs no parameterization other than the surface itself, and yet has similar storage requirements to 2D maps. In addition, it offers adaptive detail, regular sampling over the surface, and continuity across surface boundaries. The paper addresses texture creation, painting, storage, processing, and rendering with octree textures. CR Categories and Subject Descriptors: I.3.m [Computer Graphics]: Texturing; Additional Key Words: Volume Texture