Symmetries and Dynamics of Generalized Biquaternionic Julia Sets Defined by Various Polynomials

Abstract

Higher-dimensional hypercomplex fractal sets are getting more and more attention because of the discovery of more and more interesting properties and visual aesthetics. In this study, the attention was focused on generalized biquaternionic Julia sets and a generalization of classical Julia sets, defined by power and monic higher-order polynomials. Despite complex and quaternionic Julia sets, their biquaternionic analogues are still not well investigated. The performed morphological analysis of 3D projections of these sets allowed for definition of symmetries, limit shapes, and similarities with other fractal sets of this class. Visual observations were confirmed by stability analysis for initial cycles, which confirm similarities with the complex, bicomplex, and quaternionic Julia sets, as well as manifested differences between the considered formulations of representing polynomials.

Keywords

• Julia sets
• biquaternions
• fractals
• generalized Julia sets
• symmetry
• stability