Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The hypercomplex fractals obtained from generalizations of J- and M-sets, apart from their visual aesthetics, play an important role in the mathematical description in various fields of physics. The generalizations of J- and M-sets to the four-dimensional Euclidean space are well known and well described. However, very few studies were done for the higher-dimensional generalizations. The paper discusses the J-sets generalization to the hypercomplex algebra of bioctonions and completes the previous studies in this domain. The symmetry properties were studied for quadratic mapping of the bioctonionic J-sets. The discussion of limitations of the further generalizations of J-sets to higher hypercomplex spaces was also provided.
Słowa kluczowe
Rocznik
Tom
Strony
23--28
Opis fizyczny
Bibliogr. 18 poz., tab.
Twórcy
autor
- Institute of Fundamentals of Machinery Design, Silesian University of Technology Gliwice, Poland
Bibliografia
- [1] Pickover C.A., Visualization of quaternion slices, Image Vision Comput. 1988, 6, 235-237.
- [2] Norton A., Julia sets in the quaternions, Comput. Graph. 1989, 2, 267-278.
- [3] Griffin C.J., Joshi G.C., Octonionic Julia sets, Chaos Soliton. Fract. 1992, 11-24.
- [4] Griffin C.J., Joshi G.C., Transition points in octonionic Julia sets, Chaos Soliton. Fract. 1993, 67-88.
- [5] Bogush A.A., Gazizov A.Z., Kurochkin Yu.A., Stosui V.T., Symmetry properties of quaternionic and biquaternionic analogs of Julia sets, Ukr. J. Phys. 2003, 48, 295-299.
- [6] Kurochkin Yu.A., Zhukovich S.Ya., Set symmetry, generated by octonion analog of Julia-Fatou algorithm, Vestn. Brest. U. 4 - Phys. Math. 2010, 2, 74-79 (in Russian).
- [7] Mukundan R., Quaternions: from classical mechanics to computer graphics, and beyond, Proc. 7th Asian Technology Conference in Mathematics, Melaka 2002, 97-106.
- [8] Dang Y., Kauffman L.H., Sandin D.J., Hypercomplex Iterations: Distance Estimation and Higher Dimensional Fractals, World Scientific, Chicago 2002.
- [9] Yefremov A.P., Bi-quaternion square roots, rotational relativity, and dual space-time intervals, AIP Conf. Proc. 2007, 13, 178-184.
- [10] Yefremov A.P., Fundamental properties of quaternion spinors, AIP Conf. Proc. 2012, 18, 188-195.
- [11] Okubo S., Introduction to Octonion and Other Non-Associative Algebras in Physics, Cambridge University Press, Cambridge 1995.
- [12] Baez J.C., The octonions, Bull. Amer. Math. Soc. 2002, 39, 145-205.
- [13] Rios M., Jordan C*-algebras and supergravity, arXiv:1005.3514, 2010.
- [14] Conway J.H., Smith D.A., On Quaternions and Octonions: Their Geometry, Arithmetic and Symmetry, Peters, 2003.
- [15] Sabadini I., Shapiro M.V., Sommen F., Hypercomplex Analysis, Springer, Berlin 2009.
- [16] Rosenfeld B.A., Geometry of Lie groups, Springer, Dordrecht 1997.
- [17] Yaglom I.M., Complex Numbers and Its Application in Geometry, Fizmatgiz, Moscow 1963 (in Russian).
- [18] Berezin A.V., Kurochkin Yu.A., Tolkachev E.A., Quaternions in Relativistic Physics, Nauka i Tekhnika, Minsk 1989 (in Russian).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c517cd75-b800-47fb-9514-98d829b206d6