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Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik

Year 2021, Volume: 9 Issue: 3 - Additional Issue, 145 - 157, 29.05.2021
https://doi.org/10.29130/dubited.843613

Abstract

Bu çalışmada, fraktal geometrinin en önemli nesnelerinden biri olan Sierpinski üçgeninin bir genellemesi olarak düşünebileceğimiz düzensiz ölçekli bir Sierpinski üçgeni olan SG(2,3) üzerindeki içsel metriğin bir ifadesi kümenin noktalarının bu kümeye has kod temsilleri yardımıyla ifade edilmiştir.

Supporting Institution

Eskişehir Teknik Üniversitesi

Project Number

19ADP113

Thanks

Bu çalışma Eskişehir Teknik Üniversitesi Bilimsel Araştırma Projeleri tarafından desteklenmiştir (Proje no: 19ADP113).

References

  • [1] R.Hilfer ve A. Blumen, “Renormalisation on Sierpinski-type fractals,” Journal of Physics A: Mathematical and General, c. 17, s.10, ss. 537-545, 1984.
  • [2] M.T. Barlow ve B.M. Hambly, “Transition density estimates for Brownian motion on scale irregular Sierpinski gaskets,” Annales de l'Institut Henri Poincare Probabilities et Statistiques, c. 33, s. 5, ss. 531-557, 1997.
  • [3] B.M. Hambly, “Brownian motion on a random recursive Sierpinski gasket,” Ann. Probab., c. 25, ss. 1059-1102, 1997.
  • [4] S.C. Chang ve L.C. Chen, “Number of connected spanning subgraphs on the Sierpinski gasket,” Discrete Mathematics and Theoretical Computer Science, c. 11, s. 1, ss. 55-77, 2019.
  • [5] D. Burago, Y. Burago ve S. Ivanov, A Course in Metric Geometry, USA: AMS, 2001.
  • [6] M. Saltan, Y. Özdemir ve B. Demir, “An explicit formula of the intrinsic metric on the Sierpinski gasket via code representation,” Turk. J. Math., c. 42, ss. 716-725, 2018.
  • [7] M. Saltan, Y. Özdemir ve B. Demir, “Geodesics of the Sierpinski gasket,” Fractals, c. 26, s. 3, 1850024, 2018.
  • [8] Y. Özdemir, “The intrinsic metric and geodesics on the Sierpinski gasket SG(3),” Turk. J. Math., c. 43, ss. 2741-2754, 2019.
  • [9] Y. Özdemir, M. Saltan ve B. Demir, “The Intrinsic Metric on the Box Fractal,” Bull. Iran. Math. Soc., c. 45, ss. 1269-1281, 2019.
  • [10] J. E. Hutchinson, “Fractals and Self-similarity,” Indiana Univ. Math. J., c. 30, ss.713–747, 1981.
  • [11] G. Edgar, Measure, Topology and Fractal Geometry, New York: Springer, 2008.
  • [12] K.J. Falconer, “Sub-self-similar sets,” Transactions of the American Mathematical Society, c. 347, s. 8, ss. 3121-3129, 1995.
  • [13] D.W. Spear, “Measures and self-similarity.” Adv. in Math., c. 91, s. 2, ss. 143-157, 1992.
  • [14] M. Barnsley, Fractals Everywhere, San Diego: Academic Press, 1988.
  • [15] W. Sierpinski, “Sur une courbe dont tout point est un point de ramification,” C.R.Acad.Sci., c. 160, ss. 302-305, 1915.
  • [16] J. Kigami, Analysis on Fractals, Cambridge: Cambridge University Press, 2001.
  • [17] J. Gu, Q. Ye ve L. Xi, “Geodesics of higher-dimensional Sierpinski gasket,” Fractals, c. 27, s. 4, 1950049, 2019.

The Intrinsic Metric on the Scale Irregular Sierpinski Triangle SG(2,3)

Year 2021, Volume: 9 Issue: 3 - Additional Issue, 145 - 157, 29.05.2021
https://doi.org/10.29130/dubited.843613

Abstract

Project Number

19ADP113

References

  • [1] R.Hilfer ve A. Blumen, “Renormalisation on Sierpinski-type fractals,” Journal of Physics A: Mathematical and General, c. 17, s.10, ss. 537-545, 1984.
  • [2] M.T. Barlow ve B.M. Hambly, “Transition density estimates for Brownian motion on scale irregular Sierpinski gaskets,” Annales de l'Institut Henri Poincare Probabilities et Statistiques, c. 33, s. 5, ss. 531-557, 1997.
  • [3] B.M. Hambly, “Brownian motion on a random recursive Sierpinski gasket,” Ann. Probab., c. 25, ss. 1059-1102, 1997.
  • [4] S.C. Chang ve L.C. Chen, “Number of connected spanning subgraphs on the Sierpinski gasket,” Discrete Mathematics and Theoretical Computer Science, c. 11, s. 1, ss. 55-77, 2019.
  • [5] D. Burago, Y. Burago ve S. Ivanov, A Course in Metric Geometry, USA: AMS, 2001.
  • [6] M. Saltan, Y. Özdemir ve B. Demir, “An explicit formula of the intrinsic metric on the Sierpinski gasket via code representation,” Turk. J. Math., c. 42, ss. 716-725, 2018.
  • [7] M. Saltan, Y. Özdemir ve B. Demir, “Geodesics of the Sierpinski gasket,” Fractals, c. 26, s. 3, 1850024, 2018.
  • [8] Y. Özdemir, “The intrinsic metric and geodesics on the Sierpinski gasket SG(3),” Turk. J. Math., c. 43, ss. 2741-2754, 2019.
  • [9] Y. Özdemir, M. Saltan ve B. Demir, “The Intrinsic Metric on the Box Fractal,” Bull. Iran. Math. Soc., c. 45, ss. 1269-1281, 2019.
  • [10] J. E. Hutchinson, “Fractals and Self-similarity,” Indiana Univ. Math. J., c. 30, ss.713–747, 1981.
  • [11] G. Edgar, Measure, Topology and Fractal Geometry, New York: Springer, 2008.
  • [12] K.J. Falconer, “Sub-self-similar sets,” Transactions of the American Mathematical Society, c. 347, s. 8, ss. 3121-3129, 1995.
  • [13] D.W. Spear, “Measures and self-similarity.” Adv. in Math., c. 91, s. 2, ss. 143-157, 1992.
  • [14] M. Barnsley, Fractals Everywhere, San Diego: Academic Press, 1988.
  • [15] W. Sierpinski, “Sur une courbe dont tout point est un point de ramification,” C.R.Acad.Sci., c. 160, ss. 302-305, 1915.
  • [16] J. Kigami, Analysis on Fractals, Cambridge: Cambridge University Press, 2001.
  • [17] J. Gu, Q. Ye ve L. Xi, “Geodesics of higher-dimensional Sierpinski gasket,” Fractals, c. 27, s. 4, 1950049, 2019.
There are 17 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Fatma Diğdem Koparal 0000-0002-9446-9402

Yunus Özdemir 0000-0002-6890-2997

Project Number 19ADP113
Publication Date May 29, 2021
Published in Issue Year 2021 Volume: 9 Issue: 3 - Additional Issue

Cite

APA Koparal, F. D., & Özdemir, Y. (2021). Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik. Duzce University Journal of Science and Technology, 9(3), 145-157. https://doi.org/10.29130/dubited.843613
AMA Koparal FD, Özdemir Y. Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik. DUBİTED. May 2021;9(3):145-157. doi:10.29130/dubited.843613
Chicago Koparal, Fatma Diğdem, and Yunus Özdemir. “Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik”. Duzce University Journal of Science and Technology 9, no. 3 (May 2021): 145-57. https://doi.org/10.29130/dubited.843613.
EndNote Koparal FD, Özdemir Y (May 1, 2021) Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik. Duzce University Journal of Science and Technology 9 3 145–157.
IEEE F. D. Koparal and Y. Özdemir, “Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik”, DUBİTED, vol. 9, no. 3, pp. 145–157, 2021, doi: 10.29130/dubited.843613.
ISNAD Koparal, Fatma Diğdem - Özdemir, Yunus. “Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik”. Duzce University Journal of Science and Technology 9/3 (May 2021), 145-157. https://doi.org/10.29130/dubited.843613.
JAMA Koparal FD, Özdemir Y. Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik. DUBİTED. 2021;9:145–157.
MLA Koparal, Fatma Diğdem and Yunus Özdemir. “Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik”. Duzce University Journal of Science and Technology, vol. 9, no. 3, 2021, pp. 145-57, doi:10.29130/dubited.843613.
Vancouver Koparal FD, Özdemir Y. Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik. DUBİTED. 2021;9(3):145-57.