Research in Mathematical Education (한국수학교육학회지시리즈D:수학교육연구)
- Volume 8 Issue 4
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- Pages.261-277
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- 2004
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- 1226-6191(pISSN)
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- 2287-9943(eISSN)
Superior Julia Set
- Rani, Mamta (Department of Computer Science, Gurukula Kangri University) ;
- Kumar, Vinod (Department of Computer Science, Gurukula Kangri University)
- Published : 2004.12.01
Abstract
Julia sets, their variants and generalizations have been studied extensively by using the Picard iterations. The purpose of this paper is to introduce Mann iterative procedure in the study of Julia sets. Escape criterions with respect to this process are obtained for polynomials in the complex plane. New escape criterions are significantly much superior to their corresponding cousins. Further, new algorithms are devised to compute filled Julia sets. Some beautiful and exciting figures of new filled Julia sets are included to show the power and fascination of our new venture.
Keywords
- filled superior Julia set;
- superior Julia set;
- filled Julia set;
- Julia set;
- Mandelbrot set;
- topologically conjugate;
- escape criterion;
- superior escape criterion, function/Picard iteration;
- Mann iteration;
- orbit