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论文类型：期刊论文

发表时间：2007-06-01

发表刊物：Computers and Mathematics with Applications

收录刊物：EI、Scopus

卷号：53

期号：11

页面范围：1718-1732

摘要：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.