Tensor product formulation for Hilbert space-filling curves

We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed. We view a Hilbert space-filling curve as a permutation which maps two-dimensional 2ⁿtimes2ⁿ data elements stored in the row major or column major order to the order of traversing a Hilbert space-filling curve. The tensor product formula of Hilbert space-filling curves uses several permutation operations: stride permutation, radix-2 gray permutation, transposition, and antidiagonal transposition. The iterative tensor product formula can be manipulated to obtain the inverse Hilbert permutation. Also, the formulas are directly translated into computer programs which can be used in various applications including R-tree indexing, image processing, and process allocation, etc