Applications of Cantor Set to Fractal Geometry

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KARAÇAY İ. E., YÜCE S.

International Electronic Journal of Geometry, cilt.17, sa.2, ss.712-726, 2024 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.36890/iejg.1536179
  • Dergi Adı: International Electronic Journal of Geometry
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.712-726
  • Anahtar Kelimeler: Cantor set, Fractal geometry, iterated function system
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Fractal geometry is a subfield of mathematics that allows us to explain many of the complexities in nature. Considering this remarkable feature of fractal geometry, this study examines the Cantor set, which is one of the most basic examples of fractal geometry. First of all, the Cantor set is one of the basic examples and important structure of it. First, the generalization of Cantor set in on R, R2 and R3 are taken into consideration. Then, the given structures are examined over curve and surface theory. This approach enables to given a relationship between fractal geometry and differential geometry. Finally, some examples are established.