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Parikh Fuzzy vector for finite words of Rectangular Hilbert Space Filling Curve is introduced. Recurrence relations for this vector and its complement vector are produced. It is shown that the components of the Parikh Fuzzy vector are equally distributed at the limiting level. Hence, it is observed that the Parikh Fuzzy vector tends to a constant vector as n tends to infinity. Moreover, it is also valid to any other kinds of Space Filling Curves like Lebesgue Space Filling Curve, Peano Curve and Moore Curve
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