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//Derived from twinbee's algorithm
MengerSponge3(x, y, z) {//by recursively digging a box
   x=x*0.5+0.5;y=y*0.5+0.5;z=z*0.5+0.5;//center it by changing position and scale
   
   xx=abs(x-0.5)-0.5;yy=abs(y-0.5)-0.5;zz=abs(z-0.5)-0.5;
   d1=max(xx,max(yy,zz));//distance to the box
   d=d1;//current computed distance
   p=1;
   for(m=1; m<MI ; m++) {

      xa = 3*x*p % 3;
      ya = 3*y*p % 3;
      za = 3*z*p % 3;
      p*=3;

      //we can also translate/rotate (xa,ya,za) without affecting the DE estimate

      xx=0.5-abs(xa-1.5);yy=0.5-abs(ya-1.5);zz=0.5-abs(za-1.5);
      d1=min(max(xx,zz),min(max(xx,yy),max(yy,zz)))/p;//distance inside the 3 axis aligned square tubes
      
      d=max(d,d1);//intersection
   }
   return d*2; //the distance estimate. The "*2" is because of the scaling we did at the begining of the function
}

//derived from Buddhi's algorithm
SphereSponge3(x, y, z) {//by recursively digging space
   //Same as for the Menger sponge but with spheres
   x+=1;y+=1;z+=1;
   intrad=param1;
   scl=3;mod=4;
   a=x;b=y;c=z;k=2;
   d=-100;
   for (L = 0; L < MI ; L++)
   {
     xx = a * k % mod - 0.5*mod;
     yy = b * k % mod - 0.5*mod;
     zz = c * k % mod - 0.5*mod;
     r2=xx*xx + yy*yy + zz*zz;
     d1=(intrad-sqrt(r2))/k;//distance to the edge of the sphere (positive inside)
     d=max(d,d1);//intersect
     
     k *= scl;
   }
   return d;// distance estimate
}

float DE(vec3 p)
{
	p=p*0.5+vec3(0.5);
	vec3 pp= abs(p-0.5)-0.5;
	float k=1.0;
	float d1 = max(pp.x,max(pp.y,pp.z));
	float d=d1;
	for (int i = 0; i < Iterations ; i++)
	{
		vec3 pa = mod(3.0*p*k, 3.0);
		k *= Scale;
		
		pp = 0.5-abs(pa-1.5)+Offset;
             pp*=rot;
		d1=min(max(pp.x,pp.z),min(max(pp.x,pp.y),max(pp.y,pp.z)))/k;//distance inside the 3 axis aligned square tubes
		d=max(d,d1);
		if (i<ColorIterations) orbitTrap = min(orbitTrap, abs(vec4(pp,dot(pp,pp))));
	
	}
		
	// Use this to crop to a sphere:
	//  float e = clamp(length(z)-2.0, 0.0,100.0);
	//  return max(d,e);// distance estimate
	return d;
}

float DE(vec3 p)
{
	p=p*0.5+vec3(0.5);
	vec3 pp= abs(p-0.5)-0.5;
	float k=1.0;
	float d1 = max(pp.x,max(pp.y,pp.z));
	float d=d1;
	for (int i = 0; i < Iterations ; i++)
	{
		vec3 pa = mod(3.0*p*k, 3.0);
		
		pp = 0.5-abs(pa-1.5)+Offset;
             pp*=rot;
		d1= (1/k) * min(max(pp.x,pp.z),min(max(pp.x,pp.y),max(pp.y,pp.z)))/k;//distance inside the 3 axis aligned square tubes
             
		d=max(d,d1); k *= Scale;
		if (i<ColorIterations) orbitTrap = min(orbitTrap, abs(vec4(pp,dot(pp,pp))));
	
	}
		
	// Use this to crop to a sphere:
	//  float e = clamp(length(z)-2.0, 0.0,100.0);
	//  return max(d,e);// distance estimate
	return d;
}