Each side of an equilateral triangle is replaced by a four-segment bump. Iterate and the perimeter grows without bound inside a finite area.
Helge von Koch, 1904
Von Koch’s 1904 curve: replace the middle third of every segment with two sides of an equilateral bump. Each generation multiplies length by 4/3, so the perimeter is infinite while the area stays finite — the same self-similarity as a snowflake, a coastline, a tree. Motion plays the construction: the triangle grows its bumps, generation by generation, holds, then recedes.
fractal
GeneratorOne segment becomes four. Repeat on every new side and the snowflake appears.