I did not know that there were two versions of the algorithm:

> ...the algorithm we discussed here is the original algorithm given by Ken Perlin. But after a few years of giving this algorithm, he improved this in some ways, like he changed the smoothing curve, the way gradients are calculated, etc. And that will be the topic of our next article.

...and that next article doesn't exist. But:

* The 2002 paper improving it (this was likely after I first encountered Perlin noise, so I would have implemented v1!) https://mrl.cs.nyu.edu/~perlin/paper445.pdf

* A really good article explaining the v2 algorithm: https://adrianb.io/2014/08/09/perlinnoise.html