Analysis of 4D Hypercomplex Generalizations of Julia Sets

All possible 4D hypercomplex vector spaces were considered in the light of an ability of construction of Julia fractals in them. Both arithmetic fundamentals of the considered algebras as well as implementation procedures of such hypercomplex numbers are given. In the paper, the presented study summarizes well-known 4D hypecomplex fractals, like bicomplex and quaternionic ones, introduces a group of new hyper-complex fractals, like biquaternionic, and shows why other 4D hyper-complex vector spaces cannot produce the non-trivial Julia sets. All of the considered cases were enriched by several graphical representations of hypercomplex Julia sets with their graphical analysis.