Geodesic
The Generalized Biquaternionic M-J Sets
Journal for geometry and graphics, Tome 22 (2018) no. 1, pp. 49-58.

Voir la notice de l'article provenant de la source Heldermann Verlag

The Mandelbrot-Julia sets, henceforth abbreviated as M-J sets, and their properties have been extensively studied since their discovery. Many studies are focused on properties and dynamics of generalized M-J sets in complex and hypercomplex vector spaces, however there are still many variations of M-J sets which have not been studied yet. The following paper discusses one of such variations -- the M-J 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 M-J sets and their relation both with complex M-J sets as well as with their 4-space analogues: quaternionic and bicomplex M-J sets. The connectedness and dynamics of J sets is also studied. Moreover, the analysis of 3D cross-sections of J sets allows validating the relationships with other hypercomplex fractal sets and evaluating a symmetry of resulting biquaternionic sets.
Classification : 28A80
Mots-clés : Biquaternionic Mandelbrot-Julia sets, algebra of biquaternions, fractals, generalized Mandelbrot-Julia sets 
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A. Katunin . The Generalized Biquaternionic M-J Sets. Journal for geometry and graphics, Tome 22 (2018) no. 1, pp. 49-58. http://geodesic.mathdoc.fr/item/JGG_2018_22_1_JGG_2018_22_1_a5/