Intrinsic metric formulas on some self-similar sets via the code representation

Creative Commons License

Güneri M., Saltan M.

Fractal and Fractional, vol.3, no.1, pp.1-13, 2019 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 3 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.3390/fractalfract3010013
  • Journal Name: Fractal and Fractional
  • Journal Indexes: Scopus
  • Page Numbers: pp.1-13
  • Keywords: Code representation, Intrinsic metric, Self-similar sets, Sierpinski gasket
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2019 by the authors. Licensee MDPI, Basel, Switzerland.In recent years, intrinsic metrics have been described on various fractals with different formulas. The Sierpinski gasket is given as one of the fundamental models which defined the intrinsic metrics on them via the code representations of the points. In this paper, we obtain the explicit formulas of the intrinsic metrics on some self-similar sets (but not strictly self-similar), which are composed of different combinations of equilateral and right Sierpinski gaskets, respectively, by using the code representations of their points. We then express geometrical properties of these structures on their code sets and also give some illustrative examples.