ABSTRACT
The previous chapter used complex analysis to further the study of minimal surfaces. Many applications of complex numbers to geometry can be generalized to the quaternions, an extended system in which the “imaginary part” of any number is a vector in ℝ3. Although beyond the scope of this book, there is an extensive theory of surfaces defined by “quaternionic-holomorphic” curves [BFLPU]. Other uses include the visualization of fractals by means of iterated maps of quaternions extending the usual complex theory [DaKaSa, Wm2].
