Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2009-12-01

Journal: FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY

Included Journals: Scopus、EI、SCIE

Volume: 17

Issue: 4

Page Number: 427-439

ISSN: 0218-348X

Key Words: Mandelbrot Sets; Julia Sets; Multiple Critical Points; Quaternion; Fractal

Abstract: The quaternion Mandelbrot sets (abbreviated as M sets) on the mapping f : z <- z(2) + c with multiple critical points are constructed utilizing the cycle detecting method and the improved time escape algorithm. The topology structures and the fission evolutions of M sets are investigated, the boundaries and the centers of the stability regions are calculated, and the topology rules of the cycle orbits are discussed. The quaternion Julia sets with the parameter c selected from the M sets are constructed. It can be concluded that quaternion M sets have efficient information of the corresponding Julia sets. Experimental results demonstrate that the quaternion M sets with multiple critical points distinguish from that of zero critical point and the collection of the quaternion M sets with different critical points constitute the complete M sets on the mapping f : z <- z(2) + c.