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
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