Juliabulbs by bending

[msltoe]

I've lost count on the number of hours of sleep I've lost over the years looking for the Holy Grail. I know it's technically not possible, but I always wanted to be able to fuse multiple Juliabulbs together. In the past, I've managed to yz symmetrize a specific Julia set that basically behaves a lot like the burning ship. But I've never been able to symmetrize a z^2 Julia set (where b is non-zero) ... until now. As I was lying awake last night, I realized that if I bent the juliabulbs, I could match up the right polarities so I don't get the mismatched edges. I don't have a perfect bending function yet, and only Julia sets look OK so far, but here's an inner loop code that people can try out:

  if (z>0) {d = 1;z=z;} else { d = -1;z=z; }
   z = fabs(z);
   r=sqrt(z*z+y*y);
   z1 = (z*z-y*y)*r;
   y1 = (2*y*z)*r;
   z = z1+z; y = y1+y;
   z = (z)*d;
  
   r = x*x+y*y+z*z;
   x1=(x*x-y*y)*(1-z*z/r);
   y1=(2*x*y)*(1-z*z/r);
   z1=-2*z*sqrt(x*x+y*y+0.25*z*z);
   x = x1+a; y = y1+b; z = z1+c;
   iter++;

And here's a picture of [-0.8,-0.1,0]:

[KRAFTWERK]

Woahhhh!
I will not say I am happy you are sleepless msltoe but... I love that julia!
Excited to see what more lies hidden in your "bent brot"!

[msltoe]

I see some promise in this approach, but I will need new bending functions to be able to handle other seed regions. A universally-applicable bending function could lead to a good M-set.

[Nahee_Enterprises]

    I've lost count on the number of hours of sleep I've lost over the years looking for the Holy Grail.
    I know it's technically not possible, but I always wanted to be able to fuse multiple Juliabulbs together.
    In the past, I've managed to yz symmetrize a specific Julia set that basically behaves a lot like the burning ship.
    But I've never been able to symmetrize a z^2 Julia set (where b is non-zero) ... until now.   As I was lying
    awake last night, I realized that if I bent the juliabulbs, I could match up the right polarities so I don't get the
    mismatched edges.   I don't have a perfect bending function yet, and only Julia sets look OK so far, but
    here's an inner loop code that people can try out:   ...........
    And here's a picture of [-0.8,-0.1,0]:
            http://nocache-nocookies.digitalgott.com/gallery/14/803_01_10_13_3_11_42.png

    I see some promise in this approach, but I will need new bending functions to be able to handle other seed regions.
    A universally-applicable bending function could lead to a good M-set.

Very cool !!!     
With all the bending going on, I am not sure whether to refer to these as the "Kama Sutra" or "Yoga" series of fractals.  Definitely some contortionist techniques involved.     
 

[Alef]

Not bad, certain grailishness in it. Maybe two variable equations could give something.

I know it's technically not possible,

Rucker bulb seems to be closest to it.