Icaria-Noise VS Noise-Extras

It's the fastest implementation of Perlin Noise out there! I commented on all the optimizations I did over standard implementations for anyone who is interested in the details of what I did. krubbles/Icaria-Noise: A highly-optimized C# noise-function library. (github.com)

If it helps, I wrote an implementation inspired by this here: https://github.com/KdotJPG/Noise-Extras/blob/master/OpenSimplex2S_Exp.java

Periodicity is definitely a limitation of Simplex, at least without complicated skew adjustments. I wouldn't say this limitation should hold the noise back for non-periodic applications, but it certainly can't be ignored when it does come to them.

Yep! You also need to slightly adjust the grid skew so that the corners of your target square/rectangle coincide with vertices on the noise grid. Example implementation: https://github.com/KdotJPG/Noise-Extras/blob/master/OpenSimplex2S_ImprovedXZPlanes_TileableXZ.java

I have this https://github.com/KdotJPG/Noise-Extras/blob/master/OpenSimplex2S_Exp.java but it's up to you whether or not you'd consider it a good library.

Tileability is an issue, you're right. Perhaps I should have made a note on that in the article. I've made some progress in the code at this link to bring proper tileability to simplex-type. It's quite usable as-is, but it does still need work to become the best it can. In particular I need to take a closer look at performance (I accounted hard for the grid re-skewing in a way that won't make much difference given a sufficiently-large repeat period), configurability (tileable in either 2 or 3 axes), quality (mostly I could improve the primes in the hash function I used), and variety (bring this to more algos/dimensionalities).

Either way /u/pds314 I would look for a good simplex-type noise impl that supports derivatives. Here's one. Alternatively, here's a domain-rotated Perlin which addresses its square artifacts by rotating them out of the evaluation plane of focus through the extra dimension. In this, use X and Y of the 3D "ImproveXY" function" or X and Z of the 3D "ImproveXZ" function for derivatives. In the OpenSimplex2S, you can just use the 2D function with derivatives.

Code for the domain rotation in Java is here. There are various wrappers. You would want one of the methods noise4_ImproveXYZ_ImproveXY, noise4_ImproveXYZ_ImproveXZ, or noise4_ImproveXYZ. You could copy the code from these wrappers directly, or convert it to matrix form to write it compactly in GLSL. For example, noise4_ImproveXYZ_ImproveXZ would be this. Note that I'm using left multiplication so the column-major constructor format can be rearranged to show up the way you would typically write the matrix when doing linear algebra if doing right multiplication.

Depends on: this. Would also work well with this, or also this if you adapt to its features.