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Quadtree matrices using Morton-order storage provide natural blocking on every level of a memory hierarchy. Writing the natural recursive algorithms to take advantage of this blocking results in code that honors the memory hierarchy without the need for transforming the code. Furthermore, the divide-and-conquer algorithm breaks problems down into independent computations. These independent computations can be dispatched in parallel for straightforward parallel processing.Proof-of-concept is given by an algorithm for QR factorization based on Givens rotations for quadtree matrices in Morton-order storage. The algorithms deliver positive results, competing with and even beating the LAPACK equivalent.