Abstract A mathematical analysis of the structure of rotations and the dynamics of linear recurrent connectionist networks suggests a simple strategy for implementing mental rotations on a parallel distributed processing (PDP) architecture. Rather than encode a separate map for each combination of rotation axis and degree of rotation, the net embodies generators for infinitesimal rotations about three linearly independent axes. Finite rotations about an arbitrary axis are then generated in real time by the natural dynamics of the net operating under the influence of the appropriate linear combination of the three generators. The resulting transformation proceeds at a constant rate.