Cubic Hermite Curve.

https://gpfault.net/posts/perlin-noise.txt.html (1 - F(p-p0))g(p0)(p-p0) + F(p-p0)g(p1)(p-p1).

Quintic interpolation curve.

Tiling noise implementation comes from this answer: https://gamedev.stackexchange.com/questions/23625/how-do-you-generate-tileable-perlin-noise And simply takes advantage of perlin noise repeatability.