What are quaternions?
Quaternions have 4 components (1 real and 3 imaginaries) a+ib+jc+kd compared to the 2 components of complex numbers. Operations such as additions and multiplications can be performed on quaternions, but multiplication is not commutative. Quaternions satisfy the rules i2= j2 = k2= -1 ij = -ji = k jk = -kj = i ki = -ik = j When quaternions are used to write fractal formulas, the corresponding figures are in a 4D space, and obviously that constitutes a problem to draw such an image. By keeping constant one of the terms, it is possible to get a 3D “slice” of the quaternionic fractal and to draw a projection (2D) on the screen of this 3D figure (see question 4Ch). See: • Frode Gill’s quaternions page http://home.hia.no/~fgill/quatern.
