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//http://www.fractalforums.com/ifs-iterated-function-systems/revenge-of-the-half-eaten-menger-sponge/15/
float mengersponge_de(int n, vec3 pos) { //by recursively digging a box
	float x=pos.x, y=pos.y, z=pos.z;
	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

	float xx=abs(x-0.5)-0.5, yy=abs(y-0.5)-0.5, zz=abs(z-0.5)-0.5;
	float d1=max(xx,max(yy,zz)); //distance to the box
	float d=d1; //current computed distance
	float p=1.0;
	for (int i=1; i<=n; ++i) {
		float xa = mod(3.0*x*p,3.0);
		float ya = mod(3.0*y*p,3.0);
		float za = mod(3.0*z*p,3.0);
		p*=3.0;

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

		float 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*2.0; //the distance estimate. The *2 is because of the scaling we did at the beginning of the function
	return d;
}

vec3 calculate_normal(vec3 pos) {
	return -normalize(vec3(
		_DE(pos-vec_epsx) - _DE(pos+vec_epsx),
		_DE(pos-vec_epsy) - _DE(pos+vec_epsy),
		_DE(pos-vec_epsz) - _DE(pos+vec_epsz)
	));
}

dist = max(dist, dot(inputPoint,normalize(cutPlaneNormal)));

bool mengerSponge(double x2d, double y2d) {
/*
 * 1) cutting plane goes through 0.5,0.5,0.5
 * 2) plane normal is 1/√3,1/√3,1/√3, therefore vectors 1,-1,0 and 0,1,-1 are good 2D basis
 */
double x = 0.5 + x2d;
double y = 0.5 + y2d - x2d;
double z = 0.5 - y2d;

	if(x<0 || x>1 || y<0 || y>1 || z<0 || z>1 )     { return 0; } 		// point is not part of menger sponge

	int iterations=8;

	double depth=3;

	for(int iter=0; iter<iterations; iter++) {
		int holex=1;
		while(holex<depth) {
			int holey=1;
			while(holey<depth) {
				if(
					 ((x > holex/depth && x< (holex+1) /depth) && (y > holey/depth && y< (holey+1) /depth)) ||
					 ((y > holex/depth && y< (holex+1) /depth) && (z > holey/depth && z< (holey+1) /depth)) ||
					 ((x > holex/depth && x< (holex+1) /depth) && (z > holey/depth && z< (holey+1) /depth))
					 ) { return 0; }		// point is not part of menger sponge
				holey+=3;
			}
			holex+=3;
		}
		depth*=3;
	}

	return 1;	// point is part of menger sponge
}

Mandelbulb3Dv18{
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...Uz./....0..../M.0/......T....n/....E3.....g873aGCHSqD/..........m/dkpXmH....U
z.....kD12../..........wz.................................U0.....y1...sD...../..
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bx1Kxs7KrRRAzwLG4yE4QJmDU.....Y/..............sD.6....sD.6E.....................
.............oAnAt1...sD....zw1.........................................A....k1.
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zzzz.............0...................2./8.kzzzD............8....................
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................................................................................
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..............................zD................................................
................................................................................
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................4MU/4MU/................6.2........wz.........zD........kz1.....
................................................................................
............................................}
{Titel: Mandelbulb 3DckJRotate}