
Journal for Geometry and Graphics 22 (2018), No. 1, 049058 Copyright Heldermann Verlag 2018 The Generalized Biquaternionic MJ Sets Andrzej Katunin Inst. of Fundamentals of Machinery Design, Silesian University of Technology, Konarskiego 18A, 44100 Gliwice, Poland andrzej.katunin@polsl.pl The MandelbrotJulia sets, henceforth abbreviated as MJ sets, and their properties have been extensively studied since their discovery. Many studies are focused on properties and dynamics of generalized MJ sets in complex and hypercomplex vector spaces, however there are still many variations of MJ sets which have not been studied yet. The following paper discusses one of such variations  the MJ sets in the biquaternionic vector space. Starting from theoretical fundamentals on an algebra of biquaternions and its closedness under addition and multiplication, the author defines the generalized biquaternionic MJ sets and their relation both with complex MJ sets as well as with their 4space analogues: quaternionic and bicomplex MJ sets. The connectedness and dynamics of J sets is also studied. Moreover, the analysis of 3D crosssections of J sets allows validating the relationships with other hypercomplex fractal sets and evaluating a symmetry of resulting biquaternionic sets. Keywords: Biquaternionic MandelbrotJulia sets, algebra of biquaternions, fractals, generalized MandelbrotJulia sets. MSC: 28A80 [ Fulltextpdf (1500 KB)] 