Caption: "The 7 first steps of the building of the Koch snowflake in a gif animation. Notice the parallel corresponding diameters present in the inner rhomboids--yes, just notice that." (Somewhat edited.)

The Koch snowflake is a fractal.

In this animation, we see the fractal structure being built up as the surface becomes more and more corrugated.

A fractal is an geometric object that shows self-similarity. It looks the same on every scale ideally.

Many structures in nature are fractal over some range of scales to some approximation---like the coastline of Norway.

Credit/Permission: Antonio Miguel de Campos (AKA User:To campos), 2007 / Public domain.
Image link: Wikipedia: File:Von Koch curve.gif.
Local file: local link: fractal_koch_snowflake.html.
File: Mathematics file: fractal_koch_snowflake.html.