Zoom in and zoom in again,
and the same shape keeps appearing

Would you believe that no matter how much you zoom into a snowflake, an equally complex shape keeps appearing? Pull out one small piece and zoom in, and it turns out to be strikingly similar to the whole shape — this property is called self-similarity, and a shape with this property is called a fractal.

The most famous fractal, the Koch snowflake, starts from an equilateral triangle and is made by repeating a process that replaces the middle third of every edge with a pointed triangular bump. The more you repeat it, the longer the perimeter stretches, without bound, toward infinity — yet the area the snowflake occupies never grows larger than the circle enclosing the original triangle. Nature is full of shapes that resemble fractals too, like tree branches, lightning bolts, and coastlines. Increase the depth one step at a time and see this strange transformation for yourself.