Welcome to Fractal Forums

x =  x²-2yz + a
y = -z²+2xy + b
z =  y²+2xz + c

zAnotherMandelbrot3D (quaternion) {
// PLACE YOR M-BROT FORMULA HERE.
// WORKS IN BOTH 2D AND 3D.

parameter real bailout;
quaternion C;
real zx, zy, zz, zw, zzx, zzy, zzz, zzw, Cx, Cy, Cz, Cw, root2;
parameter bool testInverted;
parameter quaternion julia, perturb;
parameter int settype, power;
parameter real zheight;

// block for cutout.
parameter int iscuted;
parameter quaternion Ctaxis;
real autobailout, coordX, coordY, coordZ;

void init_once(void)
	{
// all callculated coefficients place here.
		root2=sqrt(2);
	}
	
void init(void)
 {
	
 	 if (testInverted==true && settype=="Julia Set")
	 {
	z = recip(pixel);
	C = julia;
	}
     else if (settype=="Julia Set")
    {	
	z = pixel;
	C = julia;
    }
    else if (testInverted==true && settype=="Mandelbrot Set")
	 {
	 z= perturb;
	 C= recip(pixel);
	 }
    else
    {
	z= perturb;
	C= pixel;
    } 
	
		Cx=real(C);
		Cy=imag(C);
		Cz=part_j(C);	
// for 4th dim use Cw, zw and zzw. Cw=part_k(C);
		
//block for cutout. An unelegant code.
autobailout=0;
coordX= real(Ctaxis);
coordY= imag(Ctaxis);
coordZ= part_j(Ctaxis);
if (iscuted == "Larger than") 
{
	if (coordX!=0 && real(pixel) > coordX )
	{
	autobailout= bailout +1;
	}
	if (coordY!=0 && imag(pixel) > coordY )
	{
	autobailout= bailout +1;
	}
	if (coordZ!=0 && part_j(pixel) > coordZ )
	{
	autobailout= bailout +1;
	}
}	
else if (iscuted == "Smaller than")
{
	if (coordX!=0 && real(pixel) < coordX )
	{
	autobailout= bailout +1;
	}
	if (coordY!=0 && imag(pixel) < coordY )
	{
	autobailout= bailout +1;
	}
	if (coordZ!=0 && part_j(pixel) < coordZ )
	{
	autobailout= bailout +1;
	}
}	
	 
		zx=real(z);
		zy=imag(z);
		zz=part_j(z)+ zheight;
		
}		
void loop(void)	
{

//PLACE YOUR M-BROT FORMULA HERE:
if (power=="Square")
{
zzx=zx*zx - 2*zy*zz + Cx;
zzy= - zz*zz + 2*zx*zy + Cy;
zzz= zy*zy + 2*zx*zz + Cz;
}
else if (power=="Cube")
{
zzx=zx^3 - zy^3+ zz^3 - 6*zx*zy*zz + Cx;
zzy= 3*(sqr(zx)*zy- sqr(zy)*zz-zx*sqr(zz)) + Cy;
zzz= 3*(sqr(zx)*zz+ zx*sqr(zy) -sqr(zy)*zz ) + Cz; //ERROR CORRECTED
}

	zx=zzx;
	zy=zzy;
	zz=zzz;
	
/// All three number parts are iterated seperetely, hence zzx and zx. 
		z= quaternion(zzx, zzy, zzz, 0);
		
// in 2D z is complex number so zz, zy, zz must be iterated or zz would be lost.
		
}
bool bailout(void)
	{
// cabs(z) is included for smooth bailout in 2D, abs(zzz) is included coz in 2D z is complex variable, autobailot is for cutout.
	return( cabs(z)+  abs(zzx)+ abs(zzy) + abs(zzz)+ autobailout < bailout );
	}
void description(void)
	{
this.title = "Newtonian Triplet";
this.maxiter=34;
this.helpfile="http://www.fractalforums.com/";

	bailout.caption = "Bailout Value";
	bailout.default = 12.0;
   
settype.caption = "Set type";
settype.enum = "Mandelbrot Set\nJulia Set";
settype.default = 0;

    testInverted.caption="Inverted set";
    testInverted.default=false;
	 

separator.label1.caption  = "4th value is unused.";
    julia.caption = "Julia Parameter";
    julia.default = (-0.2,0.3,0.45,0);
    //julia.visible = (settype=="Julia Set");

    perturb.caption = "Calculation Start";
    perturb.default = (0,0,0,0);
    perturb.visible = (settype=="Mandelbrot Set");
	 
    power.caption = "Power";
    power.enum = "Square\nCube";
    power.default = 0;	 
	 
	 
	zheight.caption = "Z height";
	zheight.default = 0.0;	 
	 
//block for a cutout.	 
separator.label2.caption  = "CUTS along NONZERO coordinates.";		
iscuted.caption="CUTTING";
iscuted.enum="None\nLarger than\nSmaller than";
iscuted.default= 0;
		
Ctaxis.caption ="Coordinates of cut";
Ctaxis.default= (0,0,0,0);
Ctaxis.visible = (iscuted=="Larger than" || iscuted=="Smaller than");
	}
}