Koch Snowflake Explorer

The Koch snowflake is a fractal curve with an infinite perimeter enclosing a finite area. Use the slider to increase the iteration level and observe these paradoxical properties.

Iteration (n)SidesSide LengthPerimeterArea

Box-Counting Dimension Lab

This tool estimates the fractal dimension of the snowflake's boundary using the current iteration level from the Explorer. We cover the curve with a grid of boxes of side length ε and count how many boxes, N(ε), are intersected.

N(ε) ≈ -