A New Construction of the Sierpinski Triangles with Galilean Transformations

Year 2016, Volume: 4 Issue: 1, 151 - 163, 15.04.2016

Elif Aybike Büyükyılmaz Yusuf Yaylı , İsmail Gök

https://doi.org/10.36753/mathenot.421424

Cited By: 2

Abstract

Keywords

Fractal, Dimension, Iteration, Galilean transformation

References

• [1] Akar, M., Yüce, S. and Kuruoglu, N., One-Parameter-Planar Motion in the Galilean Plane, International Electronic Journal of Geometry, Volume 6 (2003), no.1, 79-88.
• [2] Barnsley, M.F., Fractals Everywhere, 2nd ed., Academic Press, San Diego, 1993.
• [3] Barnsley, M.F., and Demko, S., "Iterated function systems and the global construction of fractals", Proc. R. Soc. London, A 399 (1985), p. 243-275.
• [4] Barnsley M. F., Devaney R. L., Benoit B. M., Pietgen H. O., Saupe D., Voss R. F., (1988), “The Science of Fractal Images”, Springer-Verlag, USA, pp. 1-20.
• [5] Barnsley M.F., et al, The science of fractal images,Springer–Verlag, New York, (1988).
• [6] Bedford T., The box dimension of self-affine graphs and repellers. Nonlinearity 1 (1989), 53-71.
• [7] Bedford T. and Urbanski M., The box and Hausdorff dimension of self-affine sets. Ergodic Theory Dynamical Systems 10 (1990), 627-644.
• [8] Edgar G.A., Measure, Topology, and Fractal Geometry, Undergraduate Texts in Mathematics, Springer-Verlag, (1990).
• [9] Falconer K J, The Geometry of Fractal Sets, Cambridge University Press (1985).
• [10] Falconer K J, Fractal Geometry, Wiley, (1990).
• [11] Falconer K. J., Fractal Geometry-Mathematical Foundations and Applications (John Wiley, 2nd ed. (2003).
• [12] Falconer K.J., The Haussdorf dimension of self-affine fractals, Math. Proc. Cambr. Phil. Soc. 103(1988), 339-350.
• [13] Falconer K.J. and Miao J., Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices, Fractals 15(2007), 289.
• [14] Hausdorff, Felix (1918), "Dimension und äusseres Mass", Mathematische Annalen 79 (1-2): 157–179.
• [15] Hutchinson J.E., Fractals and self-similarity, Indiana.Univ. Math. J. 30, 1981, pp. 713–749.
• [16] Lu. N., Fractal imaging, Morgan Kaufmann Publishers, (1997).
• [17] Mandelbrot, B., The Fractal Geometry of Nature, (1982).
• [18] Mandelbrot B. B., (1984), "The Fractal Geometry of Nature", The American Mathematical Monthly, vol. 91, no. 9, pp. 594-598.
• [19] Mandelbrot B. B., (1989), "Fractal Geometry: What Is It , and What Does It Do?", Proceedings of the Royal Society of London, vol. 423, pp. 2-16.
• [20] McMullen C., The Hausdorff dimension of general Sierpinski carpets, Nagoya Math. J. 96,(1984), pp. 1–9.
• [21] Peitgen H-O, Jürgens H and Saupe D 1992 a Chaos and Fractals: New Frontiers of Science (New York: Springer).
• [22] Peitgen H-O, Jürgens H, Saupe D, Maletsky E M, Perciante T H and Yunker L E 1991 Fractals for the Classroom:Strategic Activities Volume One (New York: Springer).
• [23] Reiter C.A., Sierpinski fractals and GCD’s Comput. Graph. 18 885–91, (1994).
• [24] Rooney J., On the three types of complex number and planar transformations, Cranfield Institute of Technology, (1978).
• [25] Taylor T.D., Connectivity properties of Sierpinski relatives, Fractals. 19(4), (2011), pp. 481–506.
• [26] Yaglom I.M. A simple non-Eucledian geometry and its physical basis: an elementary account of Galilean geometry and the Galilean principle of relativity. New-York: Springer-Verlag, (1979).
• [27] Zhou Z.L., Hausdorff measure of Sierpinski triangle, Sci. China. Ser. A. 40(10), (1997),pp. 1016-1021.