ABSTRACT
This chapter explains rich possibilities given by a tensor product operation performed on algebras, and discusses in detail several vector spaces resulting from tensor product algebras, as well as M- and J-sets constructed in them. Since such vector spaces are composed from at least two elementary vector spaces, it facetiously calls the fractal structures generated in these spaces fractal mutants. Increasing the dimensionality of the multiplied algebras used for the construction of hypercomplex fractal sets, the number of possibilities also increases. Obviously, one can construct a great variety of tensor product algebras that create vector spaces with appropriate conditions for the existence of fractal sets. Of course, many other tensor product algebras can be constructed from split algebras obtained from complex numbers, quaternions, and octonions. The chapter presents what a bicomplex fractal set looks like, the sequences of 3-D slices with a discrete step were generated.
