The use of image transformations is essential for efficient modeling and learning of visual data. But the class of relevant transformations is large: affine transformations, projective transformations, elastic deformations, ... the list goes on. Therefore, learning these transformations, rather than hand coding them, is of great conceptual interest. To the best of our knowledge, all the related work so far has been concerned with either supervised or weakly supervised learning (from correlated sequences, video streams, or image-transform pairs). In this paper, on the contrary, we present a simple method for learning affine and elastic transformations when no examples of these transformations are explicitly given, and no prior knowledge of space (such as ordering of pixels) is included either. The system has only access to a moderately large database of natural images arranged in no particular order.