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Author Topic: True 3D mandelbrot fractal (search for the holy grail continues)  (Read 48176 times)
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Fractal Fertilizer
Posts: 356

« Reply #255 on: November 19, 2010, 06:07:26 PM »

J-  thanx bunches, it's really appreciated.  I'm not worthy, of course...

Since this thread is still open, I guess it won't hurt to do a few parting shots.  The only reason I chanced on finding that code error was that I was taking the basic formula structure and editing it for a 6d version (based on CUBE roots of i) mentioned recently in an earlier post, and spotted it then.
6d really stretches FractInt's capabilities, maybe too far.  Not sure if it can do it accurately.  I don't know about opening a new thread for that.  We'll see.

Back to 4d, here are 4 pix, plotting cj by dij for a=-1.75, mag 5x, and a=-1.25, a=-.75, & a=.25, all 1x.  In each then, the center is just a, and bi=0.  Pinch points.  With the right code, even!

I downloaded ChaosPro, and if ever I can find the time, I'll see if I can learn how to get it to do this stuff.

I wouldn't mind if someone else opened a new thread based on squareroot(i) to continue this exploration, based on interest.

Proofreading hopefully final version of paper.  But of course, you've heard that "final" bit before...                    (-later!)

* CD4An175.GIF (7.26 KB, 320x200 - viewed 453 times.)

* CD4An125.GIF (7.36 KB, 320x200 - viewed 455 times.)

* CD4An75.GIF (11.26 KB, 320x200 - viewed 443 times.)

* CD4Ap25.GIF (8.32 KB, 320x200 - viewed 439 times.)
« Last Edit: November 19, 2010, 06:19:05 PM by fracmonk » Logged
Fractal Phenom
Posts: 449

« Reply #256 on: November 19, 2010, 08:16:25 PM »

If all 2d slices of your 4d object looks like the last pictures, the 3d view must be very promising.

Can you post the corrected formula? 
Fractal Fertilizer
Posts: 356

« Reply #257 on: November 24, 2010, 04:21:15 PM »

trafassel-  The formula was ok all along, but the code had an error, as I explained.  Post 251 here has the corrected views that made the pix there (not v. visible, above them). 

I was also going to mention that a by c by d plots (while b=0) will yield a handsomely symmetrical 3d object, turned 45 degress on the real axis, which splits in the middle to reveal a PERFECTLY whole M-set, a by c=d.  This is, however, is narrowed widthwise in a 1:sqrt(2) proportion.  I can't wait to see a 3d rendering, which, of course, I don't know how to do yet since I'm not familiar enough with any 3d generator...

But you might be able, no prob., I dunno...best wishes!
Fractal Phenom
Posts: 449

« Reply #258 on: November 25, 2010, 12:02:40 AM »

I can try to render your fractal. I only need the formula

For my program input i have to converted it in a formula like this (8-Mandelbulb Cos):

    public override long InSet(double ar, double ai, double aj, double br, double bi, double bj, double bk, long zkl, bool invers) {
            double aar, aai, aaj;
            long tw;
            int n;
            int pow = 8; // Mandelbulb
            double gr = 10; // Bailout value
            double theta, phi;

            double r_n = 0;
            aar = ar * ar; aai = ai * ai; aaj = aj * aj;
            tw = 0L;
            double r = Math.Sqrt(aar + aai + aaj);

            for (n = 1; n < zkl; n++) {

                theta = Math.Atan2(Math.Sqrt(aar + aai), aj);
                phi = Math.Atan2(ai, ar);
                r_n = Math.Pow(r, pow);
                ar = r_n * Math.Sin(theta * pow) * Math.Cos(phi * pow);
                ai = r_n * Math.Sin(theta * pow) * Math.Sin(phi * pow);
                aj = r_n * Math.Cos(theta * pow);

                ar += br;
                ai += bi;
                aj += bj;

                aar = ar * ar; aai = ai * ai; aaj = aj * aj;
                r = Math.Sqrt(aar + aai + aaj);

                if (r > gr) { tw = n; break; }

Fractal Senior
Posts: 6667

formerly known as 'Trifox'

« Reply #259 on: November 25, 2010, 12:57:55 AM »

sry people this thread has to be closed, threads with more than 10 pages tend to become desinformative!
open up a part II thread please!


divide and conquer - iterate and rule - chaos is No random!
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