I am trying to better understand an isometric embedding of a flat 2-Torus in $\Bbb R^3$ via a $C^1$ map. Here is a visualization involving $C^1$ fractals:
This embedding is warped by an infinite sequence of waves called corrugations, according to the Hévéa Project (thanks to @dvitek for the reference). Due to this infinity, it is unclear how the points of this surface can be defined.
My question is if this surface can be described as a function of the $x,y,z$ coordinates in $\Bbb R^3$ either in the explicit or parametric way.