TY - JOUR T1 - Düzensiz Ölçekli Sierpinski Üçgeni SG(2,3) Üzerindeki İçsel Metrik TT - The Intrinsic Metric on the Scale Irregular Sierpinski Triangle SG(2,3) AU - Özdemir, Yunus AU - Koparal, Fatma Diğdem PY - 2021 DA - May DO - 10.29130/dubited.843613 JF - Duzce University Journal of Science and Technology JO - DÜBİTED PB - Duzce University WT - DergiPark SN - 2148-2446 SP - 145 EP - 157 VL - 9 IS - 3 LA - tr AB - 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. KW - Sierpinski Üçgeni KW - Düzensiz ölçekli Sierpinski üçgeni KW - Jeodezik KW - İçsel metrik CR - [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. CR - [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. CR - [3] B.M. Hambly, “Brownian motion on a random recursive Sierpinski gasket,” Ann. Probab., c. 25, ss. 1059-1102, 1997. CR - [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. CR - [5] D. Burago, Y. Burago ve S. Ivanov, A Course in Metric Geometry, USA: AMS, 2001. CR - [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. CR - [7] M. Saltan, Y. Özdemir ve B. Demir, “Geodesics of the Sierpinski gasket,” Fractals, c. 26, s. 3, 1850024, 2018. CR - [8] Y. Özdemir, “The intrinsic metric and geodesics on the Sierpinski gasket SG(3),” Turk. J. Math., c. 43, ss. 2741-2754, 2019. CR - [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. CR - [10] J. E. Hutchinson, “Fractals and Self-similarity,” Indiana Univ. Math. J., c. 30, ss.713–747, 1981. CR - [11] G. Edgar, Measure, Topology and Fractal Geometry, New York: Springer, 2008. CR - [12] K.J. Falconer, “Sub-self-similar sets,” Transactions of the American Mathematical Society, c. 347, s. 8, ss. 3121-3129, 1995. CR - [13] D.W. Spear, “Measures and self-similarity.” Adv. in Math., c. 91, s. 2, ss. 143-157, 1992. CR - [14] M. Barnsley, Fractals Everywhere, San Diego: Academic Press, 1988. CR - [15] W. Sierpinski, “Sur une courbe dont tout point est un point de ramification,” C.R.Acad.Sci., c. 160, ss. 302-305, 1915. CR - [16] J. Kigami, Analysis on Fractals, Cambridge: Cambridge University Press, 2001. CR - [17] J. Gu, Q. Ye ve L. Xi, “Geodesics of higher-dimensional Sierpinski gasket,” Fractals, c. 27, s. 4, 1950049, 2019. UR - https://doi.org/10.29130/dubited.843613 L1 - https://dergipark.org.tr/en/download/article-file/1457946 ER -