Long time ago I played around with gimp+mathmap[1]. For some reason I needed the second derivative of a Perlin noise layer and I kind of surprised when the underlying grid structure revealed itself. I didn't know anything about the Perlin noise algorithm at the time. AFAIK there are variations of the algorithm that are continuous in the Nth derivative (for various values of N). Maybe the article's implementation is continuous in the 2nd derivative.

[1] https://www.complang.tuwien.ac.at/schani/mathmap/