An explicit formula of the intrinsic metric on the Sierpinski gasket via code representation

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SALTAN M., ÖZDEMİR Y., DEMİR B.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.2, ss.716-725, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1702-55
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.716-725
  • Anahtar Kelimeler: Sierpinski gasket, code representation, intrinsic metric
  • Anadolu Üniversitesi Adresli: Evet

Özet

The computation of the distance between any two points of the Sierpinski gasket with respect to the intrinsic metric has already been investigated by several authors. However, to the best of our knowledge, in the literature there is not an explicit formula obtained by using the code set of the Sierpinski gasket. In this paper, we obtain an explicit formula for the intrinsic metric on the Sierpinski gasket via the code representations of its points. We finally give an important geometrical property of the Sierpinski gasket with regard to the intrinsic metric by using its code representation.