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Indexed by:期刊论文

Date of Publication:2007-06-01

Journal:Computers and Mathematics with Applications

Included Journals:EI、Scopus

Volume:53

Issue:11

Page Number:1718-1732

Abstract:Fractal nature exists not only in complex plane but also in higher dimensional space. It is a focus to find new modals to construct new 3-D fractals. In this paper, the general Mandelbrot sets and Julia sets on the mapping f : z  ?zα + c (α  ?N) are discussed. The 3-D projections of M-J sets are constructed using escape time algorithm and ray-tracing method. And their properties are theoretically analysed. The connectness of the general quaternionic M sets is proved and the boundary of the stability region of the fixed point is calculated. It is found that if the parameter c of Julia sets is chosen from the M sets, they share the same cycle number and stable points. It can be concluded that the quaternionic M sets contain sufficient information of quaternionic Julia sets. © 2007.