END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

Linf=max(x,y,z)
L2=sqrt(x²+y²+z²)
mult=Linf/L2
xt=x*mult
yt=y*mult
zt=z*mult

#info Menger Distance Estimator.
#define providesInit
#include "fast-Raytracer.frag"
#include "MathUtils.frag"
#group Menger

// Number of iterations.
uniform int Iterations;  slider[0,10,20]

// Scale parameter. A perfect Menger is 3.0
uniform float Scale; slider[0.00,3,4.00]

uniform vec3 RotVector; slider[(0,0,0),(1,0,0),(1,1,1)]

// Scale parameter. A perfect Menger is 3.0
uniform float RotAngle; slider[0.00,00,360]

// Scaling center
uniform vec3 Offset; slider[(-2,-2,-2),(1,1,1),(2,2,2)]

mat3 rot;
float sc,sr;
void init() {
	rot = rotationMatrix3(normalize(RotVector), RotAngle);
	vec3 o=abs(Offset);
	sc = max(o.x,max(o.y,o.z));
	sr=sqrt(dot(o,o)+1.);
}

float DE(vec3 p)
{
#if 1
	vec3 ap=abs(p);
	float Linf=max(max(ap.x,ap.y),ap.z);//infinity norm
	float L2=length(p);//euclidean norm
	float multiplier=L2/Linf;
	p*=multiplier;//Spherify transform.
	float dd=multiplier*1.6;//to correct the DE. Found by try and error. there should be better formula.
#else
	float dd=1.;
#endif
	float r2=dot(p,p);
	for(int i = 0; i<Iterations && r2<100.; i++){
		p=abs(p);
		if(p.y>p.x) p.xy=p.yx;
      		if(p.z>p.y) p.yz=p.zy;
      		if(p.y>p.x) p.xy=p.yx;
		p.z=abs(p.z-1./3.*Offset.z)+1./3.*Offset.z;
		p=p*Scale-Offset*(Scale-1.); dd*=Scale;
		p=rot*p;
		r2=dot(p,p);	
	}
#if 1
	return (sqrt(r2)-sr)/dd;//bounding volume is a sphere
#else
	p=abs(p); return (max(p.x,max(p.y,p.z))-sc)/dd;//bounding volume is a cube
#endif
}