Karl Anders wrote:

 > Hi,


Hi :)

 > this has been discussed before, multiple times probably. I brought up the
 > question myself 3.5 years ago, though the thread strangely doesn't show
 > when you search here for "julia quaternion", see here :
 > 
http://news.povray.org/povray.general/thread/%3C3cdb6b98%40news.povray.org%3E/


Well, now that you show me its address, I remember reading that thread 
shortly after it was created, when I'd been introduced to POV-Ray for 
just a few months, and couldn't access the Internet from my own computer 
to start writing here...

Since them, I've read a little about quaternions, namely a page titled 
"Doing Physics with Quaternions" 
(http://world.std.com/~sweetser/quaternions/qindex/qindex.html), where I 
learnt that approach to them as the pair composed by a real number and 
real triplet, quite suitable for representing time and space. As was to 
be expected, your definition for the quaternion exponential function is 
identical to the one I came up with by resorting to the corresponding 4 

Lagrange-Sylvester interpolation polynomial, and the same happens 
regarding circular and hyperbolic trigonometric functions, as they can 
be defined in terms of exponentials. I've even written several macros to 
handle quaternions with all those functions and their inverses, as well 
as operating with them.

And now that I remembered this issue of quaternions in POV-Ray, I 
Google-searched the whole site, but couldn't find a single thread about 
it, so felt nothing was left but asking again from scratch...

 > The discussion then continued in personal mails between Peter Popov 
and me,
 > and the short version is:
 > - the original author of the quaternion stuff seems to have 
disappeared from
 > the net
 > - no active member (THEN, might have changed...) of the POV-team really
 > understands the quaternion-relevant code well enough to try to implement
 > new types
 > - there is a bug in the quaternion rendering that nobody can fix, for the
 > same reasons as above


What a pity... But I've seen Fractal Explorer and Quat, both of which 
provide a slightly wider variety of iterating functions, but they're all 
defined by a finite number of quaternion sums and products, or at most, 

transcendental function like the exponential, and I find this at least 
curious, and a bit disappointing...

 >> I'm also wondering why there
 >> seems to be no engine capable of rendering quaternion Mandelbrot sets...


 > One reason might be, that the "classical" Mandelbrot sets of formulas
 > pow(z,n)+c should look quite boring because any 3d-cut through them
 > orthogonal to the real axis is just a sphere ...


Well, I hadn't taken the care to realize that :) But of course, it 
wouldn't be the case of the fractal defined by the same iteration 
formula q[n+1]=f(q[n])+c as Mandelbrot's, but where you could specify an 
arbitrary quaternion q[0] as the initial term, instead of just setting 
it to zero, so achieving the same single quaternion degree of freedom 
we've got when selecting a Julia fractal for some given function.

Regards.

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