Inversions and Fractal Patterns in Alpha Plane

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GELİŞGEN Ö., ERMİŞ T.

International Electronic Journal of Geometry, cilt.16, sa.1, ss.398-411, 2023 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.36890/iejg.1244520
  • Dergi Adı: International Electronic Journal of Geometry
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.398-411
  • Anahtar Kelimeler: Alpha circle inverion, Alpha distance, Fractal, Limit set, Star-shaped set, Star-shaped set inversion
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

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