Generator

1
6
3
4
5
2
Total Dots: 0
Dice Roll: -
Waiting...

The Sierpinski Triangle

This fractal is named after the Polish mathematician Wacław Sierpiński, who described it in 1915.

What you see here is being built using the "Chaos Game" method. It proves that order can emerge from pure randomness.

The Algorithm

1. Take 3 vertices (Top, Left, Right).
2. Start at a random point.
3. Roll a die.
4. Move halfway towards the chosen vertex.
5. Draw a dot.
6. Repeat.

Dice Logic:
• Roll 1 or 2 → Move towards Top
• Roll 3 or 4 → Move towards Left
• Roll 5 or 6 → Move towards Right

Despite the random dice rolls, the points never land in the large empty triangle in the middle. They are mathematically forbidden from entering the "void".

Fractal Dimension: ≈ 1.585
This shape has zero area but infinite perimeter if iterated infinitely.