Release Time:2019-03-13  Hits:

Indexed by: Journal Article

Date of Publication: 2007-06-01

Journal: Computers and Mathematics with Applications

Included Journals: Scopus、EI

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.