A Great Need: 3-d generator for FFP 4-d M-set

[Schlega]

It is indeed a matrix equation. These will have a unique solution only when the determinant is nonzero. When the determinant is zero, there will either be no solutions or infinately many solutions.

[fracmonk]

S- Afraid I don't know calculus, and looked at the definition of determinant @ Wiki, but I'm still irretrievably lost.  I included my understanding of the situation, on the other hand, in the paper update and will try to get it up in the "grail" thread.  I really don't see a problem, as explained earlier.

[fracmonk]

Schlega-  Came up with a really good reason why you'd never find all those zeros.  It's in the latest version of the paper, notquat9.doc, now available in the "grail" thread.  Division doesn't look too realistic now at all, although that hasn't stopped many mathematicians before...you may find it an interesting read, though.

I should also mention that I cannot download your pix anywhere, and can't even print them where I am now.  So I will have to wait to study them in detail.  Sorry!

[fracmonk]

Schlega-  I noticed the pix you posted were eroding, but are now restored.  While we're on the the subject, I was wondering if higher iteration ones were tried as I suggested.  They would also need accompanying info on their orientation (which is better NOT angular for such purposes), not just which dim=0, if I am to decently compare them w. my own 2-d ones.  

Elsewise, if I have time, I may prog. a .frm file for a function involving simple div. anyway, w. my usual taste for strange things.  I am curious for deeper reasons why that part wouldn't work.

[Schlega]

I started a 1000 iteration picture, but I stopped it after a while because there was almost no visible difference from the 100 iteration version.

The pictures I made before just had an arbitrary view point, but this should help in comparing your 2D slices with mine. It shows thin slices parallel to the i-j plane as the real component goes from 0.3 to -1.4, with 0 ij component.
<a href="http://www.youtube.com/v/5tw1POeGUNU&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/5tw1POeGUNU&rel=1&fs=1&hd=1</a>

Sorry I haven't been doing much with this system lately. Unfortunately, it just doesn't look like the grail as I imagine it, so I've been trying different approaches.

[fracmonk]

Schlega-  thanx bunches for that!  I've seen some of those frames, I think...here's a curiosity I just stumbled onto over the weekend:

If you take a by c by d, with b=0, make c=d, and look at the a by c=d 2-d slice, and you'll find it turns out, (because (j+ij)/sqrt(2)=i) that you get a sideways-compressed M-set.  It's at 45 degrees to the complex plane, and simply connected.  So that extension, leaving b out, still contains M.  A single 3-d object, though it takes 4-d calculations, as other views do.  So it looks like you probably drew it first.

Only wish I was web-savvy to use such devices as the youtube animation you supplied myself.  Got to face it- i'm an old dog trying to get by on old tricks, mostly...'til later...

Also, those interested should see msg 230 in the "search for the holy grail continues" section for the "position versus sum" explanation of the zeroes.

[fracmonk]

So, getting back to it, anyone want to hear my Q&D 3-d programming idea?