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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: 1

Abstract

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.

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: 1

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.
There are 27 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Elif Aybike Büyükyılmaz This is me

Yusuf Yaylı

İsmail Gök

Publication Date April 15, 2016
Submission Date January 25, 2016
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Büyükyılmaz, E. A., Yaylı, Y., & Gök, İ. (2016). A New Construction of the Sierpinski Triangles with Galilean Transformations. Mathematical Sciences and Applications E-Notes, 4(1), 151-163. https://doi.org/10.36753/mathenot.421424
AMA Büyükyılmaz EA, Yaylı Y, Gök İ. A New Construction of the Sierpinski Triangles with Galilean Transformations. Math. Sci. Appl. E-Notes. April 2016;4(1):151-163. doi:10.36753/mathenot.421424
Chicago Büyükyılmaz, Elif Aybike, Yusuf Yaylı, and İsmail Gök. “A New Construction of the Sierpinski Triangles With Galilean Transformations”. Mathematical Sciences and Applications E-Notes 4, no. 1 (April 2016): 151-63. https://doi.org/10.36753/mathenot.421424.
EndNote Büyükyılmaz EA, Yaylı Y, Gök İ (April 1, 2016) A New Construction of the Sierpinski Triangles with Galilean Transformations. Mathematical Sciences and Applications E-Notes 4 1 151–163.
IEEE E. A. Büyükyılmaz, Y. Yaylı, and İ. Gök, “A New Construction of the Sierpinski Triangles with Galilean Transformations”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 151–163, 2016, doi: 10.36753/mathenot.421424.
ISNAD Büyükyılmaz, Elif Aybike et al. “A New Construction of the Sierpinski Triangles With Galilean Transformations”. Mathematical Sciences and Applications E-Notes 4/1 (April 2016), 151-163. https://doi.org/10.36753/mathenot.421424.
JAMA Büyükyılmaz EA, Yaylı Y, Gök İ. A New Construction of the Sierpinski Triangles with Galilean Transformations. Math. Sci. Appl. E-Notes. 2016;4:151–163.
MLA Büyükyılmaz, Elif Aybike et al. “A New Construction of the Sierpinski Triangles With Galilean Transformations”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, 2016, pp. 151-63, doi:10.36753/mathenot.421424.
Vancouver Büyükyılmaz EA, Yaylı Y, Gök İ. A New Construction of the Sierpinski Triangles with Galilean Transformations. Math. Sci. Appl. E-Notes. 2016;4(1):151-63.

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