END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

jehovajah-  I was lucky enough to unexpectedly get on a private machine for this.  Read last messages, and here's the thing: Quasz (sp?) is, if i'm correct, built from the ground up to do quat.  You may have the chops to fool it into doing this, and I'm no judge of that, but that seems WAY, WAY more complicated than it needs to be!  I "fooled" fractint into doing it by using imag(z), imag(p1), etc. to convert the i component value to real so that there are 4 real channels of computation and wrote an equivalent of the black box you saw in a previous msg. that keeps the proper relationships between components.  Absolutely true results that way, but I don't have time to do 3-d there and do not have time to get familiar w. that for a while.  But that is my BEST advice, since it's easy, straightforward, and as simple as it gets without a dedicated generator.  Saw latest pix of yours and recognized some M features.  There are surface details in the main body that don't SEEM to correspond, but might.  I can't tell so far which components are used and which is unseen, and to know what was intended may be a help.

Also, clarified point (1.) in last msg. end of previous page of this thread. These points may help demonstrate the usefulness of this system.

Actually had some leisure to look around elsewhere and found there are other extensions that preserve more properties than quaternions.  Bicomplex is one, (194 formula?) and this is not that, either.  Latest pix look look like "bicomplex".  This one seems so simple to me, I can't believe I'd be first to stumble onto it.

Still can't find it elsewhere, however.
 
Is there a way for Terry G. to review our dialogue and comment?

later, and thanx again.

Jehovajah et al- Been away in the wilderness for most of the week, and thought i'd check in.  Very surprised to see no new posts.  Anyway, I'll be doing a lot of that, since the work is seasonal.  It'll have to get cold again before I'll be able to have a look in here on any regular basis again.  I do promise to stay in touch, but don't count on quick answers if you've got any questions for me.  Be well!

@ fracmonk

Good luck and good fortune with your work, who knows you may be able to get a cheap computer out of it this year.

I noticed you are using the pixel version of the mandelbrot formula, This always adds more detail to the image if it is there. Quasz really does make this kind of thing easier once you have figured out what you want to do. Although you can not do internal slices the external detail is accurate to the chsen level.

I cannot render all the possible views that may help you to check your results as that would take too long,so i have just done top side and front view but front view has z axis going horizontal and y axis vertical.

I have tested your bail out conditions and they make no significant difference except to slow the render down.

The formula for Quasz is

[rfun
y=y#*y#
x=x#*x#
z2=imaj(z)
z1=z2*z2
w=imak(z)
wx= x#*x#-y#*y#-2*z2*w
wy=2*x#*y#+z1-w^2
wz=2*x#*z2-2*y#*w
ww=2*x#*w+2*y#*z2
rend
((z=wx+wy+wz+ww) && (|z|<130))
z=wx+wy*i+wz*j+ww*k+c
xy

xz

zy

Jehovajah- I've been thinking (watch out!) maybe I've got the Rosetta Stone that puts us on the same page.  After visiting the QuasZ site, saw his mult. tables. If you're fond of them, try this:

     i   j   ij

i  -1  ij   -j

j   ij   i   -1

ij  -j  -1  -i

When you compare them to those offered by QuasZ, notice the block of 4 in the lower right in particular.  It is why I have so little faith in the idea of bending QuasZ to do this formula for this environment.

This experience pushes me further into the suspicion that quaternions have been a delusional curse on mathematics since 1843.
W.R. Hamilton, not A. Hamilton, by the way.  I thought that absolutely hilarious from here in the states.

Anyway, if you still think you can make that program do the above, good luck.  Started looking at 2-d slices of Julias.  In M, sets are simply connected non-escaping pts or dusts w none.  Any set of 4 param coordinates not escaping should yield a Julia connected over 4 dimensions, even if not shown to be in 2 or 3.  Any view of such a set with non-escaping pts should be connected at least in that way.

This sis a polynomial rotation mandy at last.

To elaborate on last msg, no matter  what formula I might examine, I tend to gravitate toward interior pts arbitrarily near an edge.  In M, this includes minis. Structures in such places are generally more intricate.
In higher dims, say 3 for now, the equivalent is viewing pts near the surface.  In the environment I've been lately pitching here, the usual bulbs and minis of M are usually stretched and drawn, usually beyond recognition.  It's harder to say w certainty exactly WHAT features one's looking at.  Maybe bubbles and pass-thrus ARE in fact possible.  In that case, 2-d x-secs are not adequate for full overview, but valuable for looking at internal structure, if any.  It would be superb to have verifiable views in 3-d of this formula, yes?

this thread is going to be closed, or at least needs to be splitted up, please open up another thread for off topics