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r1=sqrt(sqr(sy)+sqr(sz));   // you can do x and y values here instead and generate a different fractal
                                    //  gotta make sure you change the rest of the formula to match if you decide to do so
                                    //  I prefer the way this looks, for whatever reason... anyways-
victor=complex(sx,r1)^n;   
bravo=complex(sy,sz)^n;

r3=part_i(victor)*r1^-n;

nx=part_r(victor);
ny=-abs(r3*part_r(bravo));
nz=-abs(r3*part_i(bravo));

//Then you add in your regular x pixel component and the absolute value of your y and z pixel components:

sx=nx+       (pixelr);
sy=ny+  abs  (pixeli);
sz=nz+  abs  (pixelj);    //these values are the starting values of the next iteration...

bailout= abs(sx)+abs(sy)+abs(sz)  // or square 'em if it makes you happy... doesn't make a difference to me

victor=complex(sx,sqrt(sqr(sy)+sqr(sz)));   //the major difference in this formula is that it rotates sx
bravo=complex(sqrt(sqr(sx)+sqr(sy)),sz);   // vs  sy and sz, but then calculates the sy and sz values 
cramden=complex(sx,sy);                        // using the other base mandelbrot formula... Makes an AWESOME fractal
		                                          //  you can also switch which part you do the stuff with if you so desire...
r1=cabs(cramden)^-n;
victor=victor^n;
bravo=bravo^n;
cramden=cramden^n;
		
if (r2mode) {                                      //It's neater when you exchange the y and z parts, however I put this switch in
	nx=part_r(victor);                       //  so I could do it the other way as well
	nz=-abs(part_i(bravo));
	ny=-abs(part_r(bravo)*part_i(cramden))*r1;
} else {
	nx=part_r(victor);             //this is the more interesting variety, the default...
	ny=-abs(part_i(bravo));
	nz=-abs(part_r(bravo)*part_i(cramden))*r1;
}

r1=sqrt(y^2+z^2)
sx = x^2-y^2-z^2 + pixelr
sy = 2*x*(y^2-z^2)/r1 + pixeli
sz = 4*x*y*z/r1 + pixelj

r1=sqrt(sqr(sy)+sqr(sz));	
			
			if (sy>sz) {
				z1=complex(sx,r1)^n;
				r3=r1^-n;
			} else {
				z1=complex(sx,-r1)^n;
				r3=(-r1)^-n;
			}
			if (sy*sz<0) {
				z3=complex(sx,-r1)^n;
				r4=(-r1)^-n;
			} else {
				z3=complex(sx,r1)^n;
				r4=r1^-n;
			}
			z2=complex(sy,sz)^n;
	
			nx=part_r(z1);
			ny=part_i(z1)*part_r(z2)*r3;
			nz=part_i(z3)*part_i(z2)*r4;

victor=complex(sx,sqrt(sqr(sy)+sqr(sz)));   //the major difference in this formula is that it rotates sx
bravo=complex(sqrt(sqr(sx)+sqr(sy)),sz);   // vs  sy and sz, but then calculates the sy and sz values 
cramden=complex(sx,sy);                        // using the other base mandelbrot formula... Makes an AWESOME fractal
		                                          //  you can also switch which part you do the stuff with if you so desire...
r1=cabs(cramden)^-n;