Quaternion m set with none zero critical points

Fractals

Volumn 17, Issue 4, 2009, Pages 427-439

  Sun, Yuan Yuan ^a   Wang, Xing Yuan ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Fractal; Julia sets; Mandelbrot sets; Multiple critical points; Quaternion

Indexed keywords

FRACTALS; SET THEORY; TOPOLOGY;

DETECTING METHODS; JULIA SET; MANDELBROT SET; MULTIPLE CRITICAL POINTS; PARAMETER C; QUATERNION; STABILITY REGIONS; TOPOLOGY STRUCTURE;

MAPPING;

EID: 77249112777     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218348X09004569     Document Type: Article

References (20)

1. B. B. Mandelbrot, The Fractal Geometry of Nature (W.H. Freeman, San Francisco, 1982).
2. H. O. Peitgen and D. Saupe, The Science of Fractal Images (Springer Verlag, Berlin, 1988).
3. X. Y. Wang, Chaos in Complex Nonlinear Systems, Electronic Industries (Beijing, 2003) [in Chinese].
4. A. Norton, Generation and display of geometric fractals in 3-D, Comput. Graph. 16(3) (1982) 61-67.
5. A. Norton, Julia sets in the quaternions, Comput. Graph. 13(2) (1989) 267-278.
6. J. A. R. Holbrook, Quaternionic Fatou-Julia sets, Ann. Sci. Math. Quebec 11(1) (1987) 79-94.
7. J. Gomatam, J. Doyle, B. Steves et al., Generalization of the mandelbrot set: quaternionic quadratic maps, Chaos Solitons Fractals 5(6) (1995) 971-986.
8. J. Gomatam and I. McFarlane, Generalisation of the Mandelbrot set to integral functions of quaternions, Discrete Contin. Dyn. Syst. 5(1) (1999) 107-116.
9. A. A. Bogush,A. Z. Gazizov,Y. A. Kurochkin et al., On symmetry properties of quaternionic analogs of Julia sets, in Proceedings of the 9th Annual Seminar NPCS22000 (Minsk, Belarus, 2000) pp. 304-309.
10. A. A. Bogush, A. Z. Gazizov, Y. A. Kurochkin et al., Symmetry properties of quaternionic and biquaternionic analogs of Julia sets, Ukr. Phys. J. 48(4) (2003) 295-299.
11. F. Chaitin-Chatelin and T. Meskauskas, Computation with hypercomplex numbers, Nonlin. Anal. Theor. 47(5) (2001) 3391-3400.
12. D. Rochon, A generalized Mandelbrot set for bicomplex numbers, Fractals 8(4) (2000) 355-368.
13. W. Buchanan, J. Gomantam and S. Bonnie, Generalized Mandelbrot sets for meromorphic complex and quaternionic maps, Int. J. Bifurcat. Chaos 12(8) (2002) 1755-1777.
14. N. Shizuo, Dynamics of a family of quadratic maps in the quaternion space, Int. J. Bifurcat. Chaos 15(8) (2005) 2535-2543.
15. M. Lakner, M. Skapin-Rugelj and P. Petek, Symbolic dynamics in investigation of quaternionic Julia sets, Chaos Solitons Fractals 24(5) (2005) 1189-1201.
16. α+c(α ε N), Comput. Math. Appl. 53(11) (2007) 1718-1732.
17. A. Douady and J. H. Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. Ec. Norm. Sup. 18(4) (1985) 287-343.
18. M. Romera, G. Pastor and F. Montoya, Graphic tools to analyse one-dimensional quadratic maps, Comput. Graph. 20(2) (1996) 333-339. (Pubitemid 126402690)
19. G. Pastor, M. Romera, G. Alvarez et al., How to work with one-dimensional quadratic maps, Chaos Solitons Fractals 18(5) (2003) 899-915.
20. J. C. Hart, L. H. Kauffman and D. J. Sandin, Interactive visualization of quaternion Julia sets, in Proceedings of the 1st Conference on Visualization '90 (IEEE Computer Society Press, San Francisco, California, 1990) pp. 209-218.