Rectangular Hilbert Space Filling Curve through 7-Power Free Infinite Word

Thiagarajan, K.; Navaneetham, K.; Jeyabharathi, S.

doi:10.17485/ijst/2016/v9i28/97802

Cited by 3 publications

(3 citation statements)

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“…Finite word Sn for RHSFC [9] The construction of the Rectangular Hilbert Space Filling Curve is obtained by drawing, without removing the pen from the surface of the paper to fill the rectangle of size 3 n × 2 n , an infinite succession of unit lines and double unit lines left, right, up or down. Thus the finite iterations of this curve can be represented by an finite words over the alphabet…”

Section: Rhsfc and Finite Wordmentioning

confidence: 99%

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Parikh factor matrices for finite words of rectangular Hilbert space filling curve

Bharathi¹,

Thiagarajan²,

Navaneetham³

2018

IJET

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Ordered Factor Patterns in a word over an ordered alphabet aredefined. Also, Parikh StrictlyAscending FactorMatrix and Parikh StrictlyDescending Factor Matrix of a given word are introduced. The relation of these matrices with Ordered Factor Patterns is discussed. Moreover, the ParikhStrictly Ascending FactorMatrices and the Parikh Strictly Descending FactorMatricesfor finitewords of Rectangular Hilbert Space Filling Curve are determined.

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Section: Rhsfc and Finite Wordmentioning

confidence: 99%

“…Counting ordered patterns in words generated by morphisms was done in [8]. The authors in [9] described Rectangular Hilbert Curve through 7-power free infinite word.…”

Section: Introductionmentioning

confidence: 99%

Parikh factor matrices for finite words of rectangular Hilbert space filling curve

Bharathi¹,

Thiagarajan²,

Navaneetham³

2018

IJET

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“…The authors of [7] formed different representations of fuzzy vectors. Finite words for Space Filling Curves are investigated in [9] and [10].…”

Section: Introductionmentioning

confidence: 99%

Parikh Fuzzy Vector for Finite Words of Rectangular Hilbert Space Filling Curve

Thiagarajan¹

2021

TURCOMAT

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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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