that start inside the sphere converge and none of the spheres intersect so the sphere of point i doesn't intersect with the sphere of point j so that's where we say all these spheres are non-intersecting we say x i is retrieved if the iteration equation three converged to the single fixed point in that sphere the retrieval error is the distance so you'll notice you have two things you have x i this is the actual pattern and you have x i star this is the retrieved pattern so these hopf they don't always have to