In general, it is not possible to divide a d -dimensional shape into two similarly shaped parts. Related to this parts problem is self-similarity, which means that the shape of a part is the same as the shape of the whole. When applied to a decreasing-size fractiling scheme, it means that the shape of fractiles is the same for all sizes, and when consecutive fractiles are combined, they form a larger similarly shaped fractile. An unshuffle is the inverse operation. Often computations on irregular data build a dense data structure upon whose elements a variable-size data structure is defined, e.g, the leaf boxes and the bodies that they contain.
All dimensions grow at the same rate with shuffle row-major order.
To use the card analogy, a deck is divided into d stacks and then shuffled back together by interleaving their cards. So, for instance, a four-way shuffle of yields . The unshuffled integer is divided into d segments yielding coordinates in the d -dimensional parallelepiped.