Fathauer Crystal

By: Gijs Bellaard
Created: 12 September 2019
Last modified: 05 May 2023

Description

The Fathauer Crystal is created by repeatedly placing half-sized cubes on the faces of all the cubes, starting with an unit cube.

GLSL Code

// the amount of iterations
const int ITERATIONS = 15;

// the scaling factor between iterations
const float SCALE = 2.0;

// fold normals
const vec3 N1 = normalize(vec3(1, -1, 0));
const vec3 N2 = normalize(vec3(1, 0, -1));

// distance to a unit cube
float distanceUnitCube(vec3 p)
{
  vec3 d = abs(p) - 1.0;
  return length(max(d, 0.0)) + min(max(d.x,max(d.y,d.z)), 0.0); 
}

float distanceFathauerCrystal(vec3 p)
{
    float dis = INFINITY;
    float s = 1.0;
    
    for(int i=0; i<ITERATIONS; i++)
    {
        // distance to a cube
        dis = min(dis, distanceUnitCube(p) / s);  
        
        // fold everything to the positive x axis
        p = abs(p);
        p -= 2.0 * min(0.0, dot(p, N1)) * N1; 
        p -= 2.0 * min(0.0, dot(p ,N2)) * N2; 

        // scaling
        p   *= SCALE;
        s   *= SCALE;
        
        // offset
        p.x -= SCALE + 1.0;
    }
    
    return dis; 
}