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//for every x,y,z
float ctx = fabs(x   + y   + z);
float cty =fabs(-x -y + z);
float ctz =fabs(-x + y   -z);
float ctw =fabs(x   -y -z);
x=0;
y=0;
z=0;
w=0;

for (ic=0;ic<iter;ic++){	
	const float wz=2*w*z;
	const float xy=2*x*y;
	const float X1=x*x-y*y+wz+ctx;
	const float Y1=y*y-x*x+wz+cty;
	const float Z1=z*z-w*w+xy+ctz;
	const float W1=w*w-z*z+xy+ctw;
	x=X1;
	y=Y1;
	z=Z1;
	w=W1;
	const float radius=x*x+y*y+z*z+w*w;
	if(radius>64)break;
	}

//for every x,y,z
const float ctx = (x   + y   + z);
const float cty =(-x -y + z);
const float ctz =(-x + y   -z);
const float ctw =(x   -y -z);	
x=0;
y=0;
z=0;
w=0;
float x1=0;
float y1=0;
float z1=0;
float w1=0;

	for (ic=0;ic<iter;ic++){
	const float wz=2*w*z;
	const float xy=2*x*y;
	const float wz1=2*w1*z1;
	const float xy1=2*x1*y1;
	const float X1=x*x-y*y+wz1+ctx;
	const float Y1=y*y-x*x+wz1+cty;
	const float Z1=z*z-w*w+xy1+ctz;
	const float W1=w*w-z*z+xy1+ctw;
	const float X2=x1*x1-y1*y1+wz-ctx;
	const float Y2=y1*y1-x1*x1+wz-cty;
	const float Z2=z1*z1-w1*w1+xy-ctz;
	const float W2=w1*w1-z1*z1+xy-ctw;
	x=X1;
	y=Y1;
	z=Z1;
	w=W1;
	x1=X2;
	y1=Y2;
	z1=Z2;
	w1=W2;
	if((x*x+y*y+z*z+w*w+x1*x1+y1*y1+z1*z1+w1*w1)>64)break;
	}

//for every x,y,z
float ctx = fabs(x   + y   + z)-1.35;
float cty =fabs(-x -y + z)-1.35;
float ctz =fabs(-x + y   -z)-1.35;
float ctw =fabs(x   -y -z)-1.35;
x=0;
y=0;
z=0;
w=0;

for (ic=0;ic<iter;ic++){	
	const float wz=2*w*z;
	const float xy=2*x*y;
	const float X1=x*x-y*y+wz+ctx;
	const float Y1=y*y-x*x+wz+cty;
	const float Z1=z*z-w*w+xy+ctz;
	const float W1=w*w-z*z+xy+ctw;
	x=X1;
	y=Y1;
	z=Z1;
	w=W1;
	const float radius=x*x+y*y+z*z+w*w;
	if(radius>64)break;
	}

//for every x,y,z
//I mean, for every point in the x,y,z space..
//Calculate the C constant using Quadray
float ctx = fabs(x   + y   + z);//fabs all the way
float cty =fabs(-x -y + z);//
float ctz =fabs(-x + y   -z);//
float ctw =fabs(x   -y -z);//very important..dont remove it
//
x=0;//set them to 0
y=0;//ditto
z=0;//ditto
w=0;//also important!!

//iteration loop
for (ic=0;ic<iteration;ic++){
	
     //multiply wz and xy by 2.0
	const float wz=2.0*w*z;
	const float xy=2.0*x*y;

//calculate X1,Y1,Z1,W1 using the formula and the constants ctx,cty,ctz,ctw
	const float X1=x*x-y*y+wz+ctx;
	const float Y1=y*y-x*x+wz+cty;
	const float Z1=z*z-w*w+xy+ctz;
	const float W1=w*w-z*z+xy+ctw;

//reassign to the old x,y,z,w
	x=X1;
	y=Y1;
	z=Z1;
	w=W1;//do not forget it!!..

//calculate the 4D radius..you must add the w*w here..not just x*x+ y*y + z*z.. 
	const float radius=x*x+y*y+z*z+w*w;
	if(radius>64)break;
	}

float DE(vec3 p)
{
	vec4 ct = abs(vec4(p.x+p.y+p.z,-p.x-p.y+p.z,-p.x+p.y-p.z,p.x-p.y-p.z));
	vec4 w = vec4(0.0);
	float dr = 1.0;
	float r = 0.0;
	for (int iter=0;iter<Iterations;iter++) {
		w = w*w - (w*w).yxwz + 2.0*w.wwxx*w.zzyy + ct;
	        r = length(w);
		dr = dr*r + 1.0;
		if (r > 8.0) break;
	}
	return r*log(r)/dr;
}

const float delta=7;
const double ctx =fabs(x   + y   + z)-delta;
const double cty =fabs(-x -y + z)-delta;
const double ctz =fabs(-x + y   -z)-delta;
const double ctw =fabs(x   -y -z)-delta;
float w=0;	
x=0;
y=0;
z=0;

	
for (ic=0;ic<iter;ic++){
	if(x>1)x=2-x;
	else 
	if(x<-1)x=-2-x;
	if(y>1)y=2-y;
	else 
	if(y<-1)y=-2-y;
	if(z>1)z=2-z;
	else 
	if(z<-1)z=-2-z;
	if(w>1)w=2-w;
	else 
	if(w<-1)w=-2-w;
const float vm=sqrt(x*x+y*y+z*z+w*w);
if(vm<0.5){
x=x*4;
y=y*4;
z=z*4;
w=w*4;
} else 
if(vm<1){
const float vsq=vm*vm;
x/=vsq;
y/=vsq;
z/=vsq;
w/=vsq;
}
x=x*2+ctx;
y=y*2+cty;
z=z*2+ctz;
w=w*2+ctw;
if ((x*x+y*y+z*z+w*w)>3600) break;	
}

float DE(vec3 p)
{
	vec4 ct = abs(vec4(p.x+p.y+p.z,-p.x-p.y+p.z,-p.x+p.y-p.z,p.x-p.y-p.z))-Delta;
	vec4 w = ct;
	float dr = 1.0;
	float r;
	float  r2 = length(ct);	
	for (int iter=0;iter<Iterations;iter++) {
		vec4 ww = w*w;
		w = ww - ww.yxwz + 2.0*w.wwxx*w.zzyy + ct;
		r = length(w);
		dr = dr * (r/r2) *2.0 + 1.0;
		r2 = r;
		if (r > 8.0) break;
	}
	return r*log(r)/dr;
}

const float delta=0;
const float ctx =fabs(z)-delta;
const float cty =fabs(0.86602540378443864676372317075294*x-0.5*z)-delta;
const float ctz =fabs(-0.86602540378443864676372317075294*x-0.5*z)-delta;
const float ctw =fabs(y)-delta; 
x=0;
y=0;
z=0;
float w=0;

for (ic=0;ic<Iter;ic++){
	if(x>1)x=2-x;
	else 
	if(x<-1)x=-2-x;
	if(y>1)y=2-y;
	else 
	if(y<-1)y=-2-y;
	if(z>1)z=2-z;
	else 
	if(z<-1)z=-2-z;
	if(w>1)w=2-w;
	else 
	if(w<-1)w=-2-w;

const float vm=fabs(x)+fabs(y)+fabs(z)+fabs(w);//sqrt(x*x+y*y+z*z+w*w);

if(vm<0.05){
x=x*4;
y=y*4;
z=z*4;
w=w*4;
} else 
if(vm<1.5){
const float vsq=vm*vm*vm;
x/=vsq;
y/=vsq;
z/=vsq;
w/=vsq;
}
x=2*x+ctx;
y=2*y+cty;
z=2*z+ctz;
w=2*w+ctw;

if ((x*x+y*y+z*z+w*w)>3600) break;
	
}
 

fabs(x)+fabs(y)+fabs(z)+fabs(w);//sqrt(x*x+y*y+z*z+w*w)

const float vm=fabs(x)+fabs(y)+fabs(z)+fabs(w);//here.. its the manhattan distance instead of the euclidean one..

const float vsq=vm*vm*vm;// it's raised to the cube.. :)