Koch snowflake

The word comes from the Latin fractus, meaning broken or fragmented, but the ideas do go back further.

In 1904, Helge von Koch created the Koch snowflake.

You start with a triangle, add smaller triangles to each side, repeat forever, and you get an infinite perimeter in a finite space, and the pattern looks the same at every zoom.

So that was in 1904.

However, that exponent isn't always equivalent to the apparent number of dimensions of the space the object exists in.

Take the case of fractals, or objects that have ever more detailed structure as you zoom in, such as the Koch curve or Koch snowflake.

In these cases, the smaller the boxes are, the more structure there is for them to line up along, so they scale differently.

The exponent of r in the scaling law is a fraction, which indicates how much new structure is revealed as you zoom in.