Houdini VEX - Sierpinski Triangle Algorithm

Inspired by a TikTok video that talks about the Sierpinski Triangle Algorithm. I’m recreating it in Houdini.

int points_to_generate = chi("Points");
vector positions[];
resize(positions, points_to_generate);

// Initial three vertices of the triangle from your input points
vector p1 = point(0, "P", 0);  // (0.0, 1.0, 0.0)
vector p2 = point(0, "P", 1);  // (0.866025, -0.5, 0.0)
vector p3 = point(0, "P", 2);  // (-0.866025, -0.5, 0.0)

// Start with a random point inside the triangle
vector current = p1;  // You can start anywhere, it will converge

// Generate points using the chaos game algorithm
for(int i = 0; i < points_to_generate; i++) {
    // Pick a random vertex (1, 2, or 3)
    float rand = random(i);
    vector target;
    
    if(rand < 0.333) {
        target = p1;
    } else if(rand < 0.666) {
        target = p2;
    } else {
        target = p3;
    }
    
    // Move halfway to the chosen vertex
    current = (current + target) * 0.5;
    
    // Store the new point
    positions[i] = current;
}

// Create points from the generated positions
for(int i = 0; i < points_to_generate; i++) {
    addpoint(0, positions[i]);
}