There are six patent claims that I have no interest in reading. Apparently there is also an OpenSimplex noise for circumventing the patent, but it only goes up to 4D [simplex usefully goes up to 5D].
I was caught off guard by this! It just always felt like simplex noise was just perlin v2 and I never thought twice about the legal status of it. The 2022-01-08 Anticipated expiration is definitely something to look forward to here, especially since the current owner (an investment firm) appears to have >100 ongoing patent litigation cases, with patents as vague as network load balancing.
Reading the patent itself, there's definitely some weirdness to it, like how specific it is about application to texturing. I believe heightmaps would be acceptable (IANAL).
In slightly unrelated news, a bunch of Microsoft patents on fonts expired last October.
It's worth noting that OpenSimplex has different characteristics to Simplex in higher dimensions. Specifically some have noticed a stark tendency to form orbs in 4D, so it's definitely worth comparing the output of all 3 (perlin, simplex, and OpenSimplex) to see if they give you what you're looking for.
Additionally, it may or may not be legally distinct (hasn't been tested).
There are six patent claims that I have no interest in reading. Apparently there is also an OpenSimplex noise for circumventing the patent, but it only goes up to 4D [simplex usefully goes up to 5D].