New formula: Type I (I as in eye, not one)

[M Benesi]

The first 8 are of the front of the fractal, straight on, same size (different options selected).  There is r2mode, sumode, and sumode2 (I use absmode boolean variable, put absmode/sumode 2 as a descriptor in the full formula package which will be updated at some point).  Since there are 3 on/off switches (that can be set all off, all on, or any variety...) there are 2^3=8 different fractal types (of the same basic formula).  I'm liking the sumode+r2mode variety for it's extra starfishes around the big one (for z^9)...  but r2mode unchecked may be the best bet.

The first 8 are all z^8, 5 iterations, "front side" of the fractal looking towards the positive x axis (which would be pointy side of a z^2 Mandelbrot, of course, if you looked directly at it, as the z^2 Mandelbrot is 2 dimensional, you would see nothing). 









a couple of rear shots (2 different modes):


Small side shot:

Code:

if (fractaltype=="Type I") {
		if (r2mode) {    
		r2=(sqr(sx)+sqr(sy)+sqr(sz))^(n/2);
		r1=(sqr(sx)+sqr(sy2)+sqr(sz2))^(n/2);
		} else {
		r2=(sqr(sx)+sqr(sy)+sqr(sz))^(n/2);
		}
		theta=atan2(sx+flip(sy));
		whiskey=atan2(sx+flip(sz));
		tango=atan2(sx+flip(sqrt(sy2^2+sz2^2)));
		foxtrot=atan2(sy2+flip(sz2));
		
	
		if (sumode) {
		    if (r2mode) {
			 if (absmode) {  //sumode 2
				nx=r2*cos(tango*v)*cos(theta*v)*cos(whiskey*v);
				} else {
				nx=r2*cos(tango*v);
				}
			ny=r1*sin(theta*v);
			nz=r1*sin(whiskey*v);
			ny2=r2*cos(foxtrot*v)*sin(tango*v);
			nz2=r2*sin(foxtrot*v)*sin(tango*v);
			} else {
			if (absmode) {  //sumode 2
				nx=r2*cos(tango*v)*cos(theta*v)*cos(whiskey*v);
				} else {
				nx=r2*cos(tango*v);
				}
			ny=r2*sin(theta*v);
			nz=r2*sin(whiskey*v);
			ny2=r2*cos(foxtrot*v)*sin(tango*v);
			nz2=r2*sin(foxtrot*v)*sin(tango*v);
			}
		} else {
			if (r2mode) {
			if (absmode) {  //sumode 2
				nx=r2*cos(tango*v)*cos(theta*v)*cos(whiskey*v);
				} else {
				nx=r2*cos(tango*v);
				}
			ny=r2*sin(theta*v);
			nz=r2*sin(whiskey*v);
			ny2=r1*cos(foxtrot*v);
			nz2=r1*sin(foxtrot*v);
			} else {
			if (absmode) {  //sumode 2
				nx=r2*cos(tango*v)*cos(theta*v)*cos(whiskey*v);
				} else {
				nx=r2*cos(tango*v);
				}
			ny=r2*sin(theta*v);
			nz=r2*sin(whiskey*v);
			ny2=r2*cos(foxtrot*v);
			nz2=r2*sin(foxtrot*v);
			}
		}
		
		if (juliaMode) {
		sx=nx+cr;
		sy=ny+ci;
		sz=nz+cj;
		sy2=ny2+ci;
		sz2=nz2+cj;
		} else {
		sx=nx+(pixelr);
		sy=ny+abs(pixeli);
		sz=nz+(pixelj);
		sy2=ny2+abs(pixeli);
		sz2=nz2+(pixelj);
		}
	
		bail=abs(sx)+abs(sy)+abs(sz);
		z=quaternion(sx,sy,sz,0);
	}

[M Benesi]

  Just a few quick shots, type I is compute-intensive.

  First, a little shot of the front "Mandelbrot" bulb thing, then a nice shot of elephant valley.  The front has good fractal variety... the rear (elephant valley area) does too (but it is still quicker to set a high z^n value, as they need less iterations so are less compute intensive).  Haven't done a side zoom yet...
Front thingy:

Elephant valley:

Quick dirty zoom on the front stalk:

[KRAFTWERK]

Beautiful!

[M Benesi]

Thanks   

[Rathinagiri]

Wonderful!

[M Benesi]

  Thanks Rathinagirl,

  Here are a few (bad coloring) z^2 of a new "subtype" of the formula (with sumode checked):
  I'll post full code later, for now, just put this in (and add rXmodec boolean parameter to variable initialization area) before the last r2= statement (after the else after if (r2mode)....) and a } after the last r2= statement. or .. I should just post the code.  It follows (just replace the r2 assignment part).

  Use rXmodec + sumode for AWESOMENESS.  Even the z^2 has interesting patterns emerging, although it takes a few iterations (by a few I mean a lot of compute cycles).  It's much quicker to go to higher z^n because they take less iterations for patterns to emerge.  As a matter of fact, I'll post a z^5 as a stand alone... because rXmodec + sumode type I is awesome.

Code:

if (r2mode) {
		  if (rXmodeb) {
		  	r1=(sqr(sx)+sqr(sy)+sqr(sz))^(n/2);
			r2=(sqr(sx)+sqr(sy2)+sqr(sz2))^(n/2);
			} else {
			r2=(sqr(sx)+sqr(sy)+sqr(sz))^(n/2);
			r1=(sqr(sx)+sqr(sy2)+sqr(sz2))^(n/2);
			}
		} else {
			if (rXmodeb) {
			r2=(sqr(sx)+sqr(sy)+sqr(sz)+sqr(sy2)+sqr(sz2))^(n/2);
			} else {
			   if (rXmodec) {
				r2=(sqr(sx)+sqr(sy2)+sqr(sz2))^(n/2);
				} else {
				r2=(sqr(sx)+sqr(sy)+sqr(sz))^(n/2);
				} 
			}
		} 

  Notice the swirls forming near the axis.  It starts forming more complicated swirls off the swirls (swirlpools... really) as you increase iterations.  

  Some more elephant swirls (the first are below... but... dunno, I chose to put the newer ones first):





  
This is just a nice front shot of the new mode (rXmodec).  It really has quasi-Mandelbrot goodness on both ends, maybe on the sides as well (haven't checked them too much, but assume the outcroppings have some interesting features, as the rest of the fractal is simply phenomenal, as far as fractals go).

And here is a shot of another part of the elephant valley side (bigger):