ABSTRACT
This chapter explains the world of creatures and beasts living in higher-dimensional vector spaces, which sometimes have weird, but still self-similar and very complex in a geometrical sense, shapes. In spite of their young age, such hypercomplex fractals gained great popularity among the fractal community, both scientists and computer graphics artists. One of the approaches to constructing hypercomplex fractals uses hypercomplex vector spaces, namely, the spaces defined by the algebra of quaternions and octonions. The chapter discusses that the higher-dimensional algebras in this approach cannot be used for construction of hypercomplex fractals. The second approach assumes the construction of hypercomplex fractals using Clifford algebras, which are not limited as the normed division ones. The Clifford algebras are named after their discoverer, William Kingdon Clifford, who worked on higher-dimensional generalizations of quaternions proposed by Hamilton. The chapter describes the hypercomplex numbers and a specificity of construction of fractals based on them.
