In this paper we propose the use of fractals and especially the Hilbert curve, in order to design good distance-preserving mappings. Such mappings improve the performance of secondary-key- and spatial- access methods, where multi-dimensional points have to be stored on an 1-dimensional medium (e.g., disk). Good clustering reduces the number of disk accesses on retrieval, improving the response time. Our experiments on range queries and nearest neighbor queries showed that the proposed Hilbert curve achieves better clustering than older methods ("bit-shuffling", or Peano curve), for every situation we tried. (Also cross-referenced as UMIACS-TR-89-47)