• DocumentCode
    1804720
  • Title

    Research on Misiurewiz points in Mandelbrot set

  • Author

    Tao, Sui ; Zhang Ze-yang ; Ze-yang, Zhang ; Ming-hao, Tian

  • Author_Institution
    Sch. of Inf. Sci. & Eng., Shenyang Li-gong Univ., Shenyang, China
  • Volume
    4
  • fYear
    2011
  • fDate
    24-26 Dec. 2011
  • Firstpage
    2188
  • Lastpage
    2191
  • Abstract
    Misiurewiz points and attracting points of the chaotic regions in the Mandelbrot set are located in what we call shrubs. Certain branch points are Misiurewicz points (including all "obvious" branch points in the filaments) and certain terminal points are also Misiurewicz points. Using the method of computer mathematic experiments , The distribution rules of Misiurewiz points in Mandelbrot set generated by the complex mapping z←z2 +c are studied. In this paper, we have focused on the method of solving about Misiurewiz points which located in the Mandelbrot set, and also shows the relationship for Misiurewiz point and Tree trunk of Misiurewiz points with recurrence formula. We have seen that each shrub is made up of infinite chaotic-bands, Including countless Misiurewiz points and periodic buds. it provides a new way on discussing internal structure of Mandelbrot set.
  • Keywords
    set theory; trees (mathematics); Mandelbrot set; Misiurewiz points; chaotic region; infinite chaotic-bands; recurrence formula; shrubs; tree trunk; Chaotic bands; Mandelbrot set; Misiurewiz points; Periodic buds; Topology relationship;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Computer Science and Network Technology (ICCSNT), 2011 International Conference on
  • Conference_Location
    Harbin
  • Print_ISBN
    978-1-4577-1586-0
  • Type

    conf

  • DOI
    10.1109/ICCSNT.2011.6182410
  • Filename
    6182410