Sierpinski tetrahedron attempt

#define DE_ITER 10
#define MARCHING_ITER 64
#define MARCHING_THRESHOLD 10e-6

vec3 camera = vec3(0., 1., -5.);

float d_sierpinski_tetrahedron(vec3 z)
{
    float Scale = 0.5;
    vec3 a1 = vec3(1,1,1);
    vec3 a2 = vec3(-1,-1,1);
    vec3 a3 = vec3(1,-1,-1);
    vec3 a4 = vec3(-1,1,-1);
    vec3 c;
    int n = 0;
    float dist, d;
    while (n < DE_ITER) {
         c = a1; dist = length(z-a1);
            d = length(z-a2); if (d < dist) { c = a2; dist=d; }
         d = length(z-a3); if (d < dist) { c = a3; dist=d; }
         d = length(z-a4); if (d < dist) { c = a4; dist=d; }
        z = Scale*z-c*(Scale-1.0);
        n++;
    }

    return length(z) * pow(Scale, float(-n));
}

float d_plane(vec3 p, vec3 e1, vec3 e2, vec3 a)
{
    e1 = normalize(e1);
    e2 = normalize(e2);
    vec3 pp = dot(p, e1) * e1 + dot(p, e2) * e2 + a;
    return length(p - pp);
}

float d_sphere(vec3 p, vec3 c, float r)
{
    return length(p - c) - r;
}

float DE(vec3 p)
{
    // return d_sphere(p, vec3(cos(time), sin(time), cos(time)), 1.);
    return d_sierpinski_tetrahedron(p);
    // return min(d_plane(p, vec3(1., 0., 0.), vec3(0., 0., 1.), vec3(0.)), d_sphere(p, vec3(cos(time), sin(time), cos(time)), 1.));
}

void main()
{
    vec2 uv = (in_uv_coords - vec2(0.5, 0.5)) * 2;
    vec3 dir = normalize(vec3(uv, 1.));
    int i;
    float d = 0;
    bool ended = false;
    for(i = 0; i < MARCHING_ITER; i++)
    {
        vec3 p = camera + d * dir;
        float dd = DE(p);
        d += dd;
        if(abs(dd) < MARCHING_THRESHOLD)
        {
            ended = true;
            break;
        }
    }

    if(ended) gl_FragColor = vec4(1., 1., 1., 0.) * (1. - (float(i) / float(MARCHING_ITER)));
    else gl_FragColor = vec4(0., 0., 0., 0.);
}