Begin with an equilateral triangle.

Scale it by a factor of 1/3 and place from IFF BROCHURE
copies of the smaller triangles along each side of the original. Scale again by 1/3, and once more place copies of the smaller triangles along all sides of the larger figure. Repeat ad infinitum. The edge of the Koch Snowflake – the so called Koch Curve - and was the first fractal form discovered.

Image of a Koch Curve

“It is this similarity between the whole and its parts, even infinitesimal ones, that makes us consider this curve of von Koch as a line truly marvelous among all. If it were gifted with life, it would not be possible to destroy it without annihilating it whole - for it would be continually reborn from the depths of its triangles, just as life in the universe is.”

- Ernesto Cesaro (1905)

Atti della R. Accad. Sc. Fis. Math. NapoliThough finite in geometric extent, the Koch curve is infinite in length. Like other fractal curves it is poised between a line and a plane, a topological ambiguity that enables its depthless internal complexity. Where a line has one dimension and a plane has two, the Koch curve has a “fractional” dimension of 1.26. Coastlines, clouds and other fractal structures all possess a fractional dimension. The dimension of the west coast of Britain has been measured at 1.25.