Advertisement

Burning Ship and Its Quasi Julia Images Using Mann Iteration

  • Shafali Agarwal
  • Ashish Negi
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 235)

Abstract

An invented form of Mandelbrot set came into existence in 1992 when Michelitsch and Rossler have applied seemingly small changes in complex analytic Mandelbrot set function and got an image resembled to a ship going into flame. He named it burning ship. Our goal in this paper is to apply Mann Iteration method to burning ship function and produce a collection of stunning images. We have also calculated the fixed points of such images to measure the convergence rate and those fixed points can be further useful in various fractal applications such as fractal cryptography. Hence we are in position to examining numerically the stability of the fractals.

Keywords

Mann Iteration M-Burning Ship Quasi Julia Set Fixed Point 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ewing, J.H.: can we see the Mandelbrot Set. The College Mathematics Journal 26(2), 90–99 (1995)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Ewing, J.H., Schober, G.: The area of Mandelbrot Set. Numerische Mathematik 61, 59–72 (1992)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Garmendia, A., Salvador, A.: Fractal dimension of birds population size time series. Science Direct, Mathematical Bioscience 206, 155–171 (2007)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Mandelbrot, B.B.: Fractal Aspects of the Iteration of z-> λz (λ-z) for Complex 2. Z. Ann. NY Acad. Sci. 357, 249 (1980)CrossRefGoogle Scholar
  5. 5.
    Michelitsch, M., Rossler, O.E.: Spiral structures in Julia sets and related sets. In: Hargittai, I., Pickover, C.A. (eds.) Spiral Symmetry, pp. 123–134. World Scientific, Singapore (1992)Google Scholar
  6. 6.
    Michelitsch, M., Rossler, O.E.: The Burning Ship and Its Quasi Julia Sets. Chaos and Fractals: Computer & Graphics 16(4), 435–438 (1992)CrossRefGoogle Scholar
  7. 7.
    Negi, A., Rani, M.: Midgets of Superior Mandelbrot set. Chaos, Solitons, and Fractals 36, 237–245 (2008)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Peitgen, H.O., Richter, P.: The Beauty of Fractals: Images of Complex Dynamical Systems. Springer, Heidelberg (1986)CrossRefMATHGoogle Scholar
  9. 9.
    Rana, R., Dimri, R.C., Tomar, A.: Remarks on Convergence among Picard, Mann and Ishikawa iteration for Complex Space. International Journal of Computer Applications (0975-8887) 21(9), 20–29 (2011)CrossRefGoogle Scholar
  10. 10.
    Rani, M., Kumar, V.: Superior Mandelbrot sets. J. Korea Soc. Math. Educ. Ser. D, Res. Math. Educations, 279–291 (2004)Google Scholar
  11. 11.
    Rani, M., Kumar, V.: Superior Julia set. J. Korea Soc. Math. Educ. Ser D Res. Math. Educations 8(4), 261–277 (2004)Google Scholar
  12. 12.
    Rossler, O.E., Kahlert, C., Parisi, J., Peinke, J., Rohricht, B.: Hyperchaos and Julia sets. Zeitschrift Naturforschung Teil A 41, 819–822 (1986)Google Scholar
  13. 13.

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.JSS Academy of Technical EducationNoidaIndia
  2. 2.Dept. of Computer ScienceG.B. Pant Engg. CollegePauri GarwalIndia

Personalised recommendations