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On the symmetry of bioctonionic Julia sets

Katunin A.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 2

23--28

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.