# Sierpinski Tetrahedron

By: Gijs Bellaard

## Description

The Sierpinski Tetrahedron is made by repeatedly replacing the four corners of all the tetrahedrons with half-sized tetrahedrons.

## GLSL Code

```
//The amount of iterations
const int ITERATIONS = 15;
//The scaling factor between iterations
const float SCALE = 2;
//Fold normals
const vec3 N1 = normalize(vec3(1,1,0));
const vec3 N2 = normalize(vec3(1,0,1));
const vec3 N3 = normalize(vec3(0,1,1));
float distanceSierpinskiTetrahedron(vec3 p){
float s = 1.;
for(int n=0; n<ITERATIONS; n++) {
//Folds
p -= 2.*min(0.,dot(p,N1))*N1;
p -= 2.*min(0.,dot(p,N2))*N2;
p -= 2.*min(0.,dot(p,N3))*N3;
//Scaling
p *= SCALE;
s *= SCALE;
//Offset
p -= -1.;
}
//Distance to a tetrahedron
float d = distanceTetrahedron(p);
return d/s;
}
```