Noise Generation

Value noise

As a final piece of research, I implemented these three value noise types. They are incredibly useful and versatile, and because of that, are used very often. Besides this, with a little added effort, they can be made repeatable.
Here you have Voronoi, Perlin, and Simplex:

Octaves

Additionally, they are neat, as you can layer multiple "octaves" of them to create highly detailed noise, often used for terrain or textures.
Here you have higher octaves of Voronoi, Perlin, and Simplex:

Interpolation

Finally, a very neat trick that can be performed when calculating these textures is to also generate their normals. Since value noise is normally a function of position, we can take the integral of the method used. This gives us an analytical approach to determine the normals, which is much better than using screen-space solutions.
Here you have normals of Voronoi, Perlin, and Simplex:

Here you have higher octaved normals of Voronoi, Perlin, and Simplex: