Menger Sponge

https://scrapbox.io/files/65f2b5ca95822600268936fb.png

code:menger_sponge_sdf.glsl

// distance to a menger sponge of n = 1

float crossDist( in vec3 p ) {

vec3 absp = abs(p);

// get the distance to the closest axis

float maxyz = max(absp.y, absp.z);

float maxxz = max(absp.x, absp.z);

float maxxy = max(absp.x, absp.y);

float cr = 1.0 - (step(maxyz, absp.x)*maxyz+step(maxxz, absp.y)*maxxz+step(maxxy, absp.z)*maxxy);

// cube

float cu = max(maxxy, absp.z) - 3.0;

// remove the cross from the cube

return max(cr, cu);

}

// menger sponge fractal

float fractal( in vec3 p ) {

float scale = 1.0;

float dist = 0.0;

for (int i = 0 ; i < FRACTAL_ITER ; i++) {

dist = max(dist, crossDist(p)*scale);

p = fract((p-1.0)*0.5) * 6.0 - 3.0;

scale /= 3.0;

}

return dist;

}

Livecoded

code:menger_sponge_sdf.glsl

float cd( in vec3 p ) {

p = abs(p);

float d=0.,m;

for(int i=0;i++<3.;){

d+=step(m=max(p.y,p.z),p.x)*m;

p = p.yzx;

}

return max(max(p.x,max(p.y,p.z))-3,1.-d);

}

// menger sponge fractal

float fractal( in vec3 p ) {

float s = 1.,d=0.;

for (int i=0;i<6;i++){

d = max(d, cd(p)*s);

p = fract((p-1.)*.5)*6.-3.;

s /= 3.0;

}

return d;

}