Order from Randomness
We place 3 fixed points in a triangle (labeled A, B, C). We also put a "pen" at a random spot on the screen to start (the white dot).
Every step, we do exactly the same thing -
Try the +1 Step button to see this visualized!
You might think jumping randomly would create a messy cloud. But jumping halfway creates a "Forbidden Zone."
No matter where you start, you can never jump into the large upside-down triangle in the middle. By repeating this, you create smaller and smaller forbidden zones forever. This is called the Sierpiński triangle.
This creates a Fractal—a shape made of smaller copies of itself.
Generated by Gemini