Inversions and Fractal Patterns in Alpha Plane

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International Electronic Journal of Geometry, vol.16, no.1, pp.398-411, 2023 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.36890/iejg.1244520
  • Journal Name: International Electronic Journal of Geometry
  • Journal Indexes: Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.398-411
  • Keywords: Alpha circle inverion, Alpha distance, Fractal, Limit set, Star-shaped set, Star-shaped set inversion
  • Eskisehir Osmangazi University Affiliated: Yes


In this paper, we introduce the α−circle inversion by using α−distance function instead of Euclidean distance in definition of classical inversion. We give some proporties of α−circle inversion. Also this new transformation is applied to well known fractals. Then new fractal patterns are obtained. Moreover we generalize the method called circle inversion fractal be means of the α−circle inversion. In alpha plane, R2 α, we give a generalization of α−circle inversion fractal by using the concept of star-shaped set inversion which is a generalization of circle inversion fractal