Better understanding of Simplex Noise

Better understanding of Simplex Noise

Well it's needless to say that I've recently found simplex noise. The
algorithm for an absolute different amount of possibilities and so on
which is great for creating textures, height maps and time-dependent
graphics.
I already have the function in the program and it works wonders, the
problem is that as a "mathematician" I just can't stand not understanding
thoroughly how the function works.
Basically the only thing I don't really understand is if the "skewed"
coordinates are the coordinates of the simplical or orthogonal grid. And
also that if the inputs define which of these grids: the simplical or
orthogonal.
I'm certain I could figure the rest out but I just don't understand which
grid belongs to which coordinates. Also any video, book, link that at
least shows a visual step-by-step process would be very useful.
Note:
If a questions or doubt arises please leave a comment. Thanks!!!