After explaining the details of an efficient technique, developed in early 1980s, to plot digital images of quaternion filled-in Julia sets, later considerations on it will introduce a new modification for displaying such sets with no interior too. A step by step description via pseudo-C++ is given. The reader is assumed to be familiar with advanced programming and quaternion calculus.

As we know, quaternions are very efficient for representing rotations with clear geometric meaning (rotation axis and angle) and only one redundancy. Unfortunately, they do not handle translations, which meanwhile can be made multiplicative along with rotations via the use of homogeneous coordinates. Despite also being 4-tuples, homogeneous coordinates are algebraically incompatible with quater...

In the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} ‎{underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$‎. ‎By this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎When the‎ ‎matrix equation is consistent over...

This paper is concerned with quaternion-valued functions on the plane and operators which act on such functions. In particular, we investigate the space L(R,H) of square-integrable quaternion-valued functions on the plane and apply the recently developed Clifford-Fourier transform and associated convolution theorem to characterise the closed translation-invariant submodules of L(R,H) and its bo...

The main objective of this article is to give a survey on elementary functions in the context of quaternionic analysis. We define some of their more common properties, which as in the real and complex cases, will be familiar to the reader. This leads to the consideration of quaternion-valued functions depending on a quaternion variable, that is, functions whose input and output are quaternions....