Infinite Detail

Sierpinski and Koch

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Fractals repeat their pattern at every scale (self-similarity).
• Sierpinski: the area shrinks to zero, but the shape persists.
• Koch snowflake: infinite perimeter enclosing a finite area.

Steps

1. The Sierpinski triangle
2. Area left
3. The Koch snowflake
4. Zooming forever
5. Fractal trees
6. Total length
7. Infinite coastline