I can wrap my head around using a 2D Perlin noise function to generate the height value but I don't understand why a 3D Perlin noise function would be used. In Notch's blog, he mentioned using a 3D Perlin noise function for the terrain generation on Minecraft. Does anyone know how that would be done and why it would be useful? If you are passing x, y, and z values doesn't that imply you already have the height?
Well, Minecraft is about Mines. So, what Notch tried to solve was: "How do I get holes / overhangs in my world?"
Since 2D perlin noise generates nice/smooth looking hills, 3d perlin noise will generate nice/smooth hills and nice holes in your 3D voxel grid.
An implementation can be found here (while that is an N-dimensional solution).
In other use-cases the Z component of a 3D perlin noise is set to the current time. This way you will get a smooth transition between different 2d perlin noises and that can be used as groundwork for fluid textures.
The article says exactly why he used 3D noise:
I used a 2D Perlin noise heightmap... ...but the disadvantage of being rather dull. Specifically, there’s no way for this method to generate any overhangs.
So I switched the system over into a similar system based off 3D Perlin noise. Instead of sampling the “ground height”, I treated the noise value as the “density”, where anything lower than 0 would be air, and anything higher than or equal to 0 would be ground.
来源：https://stackoverflow.com/questions/6091468/how-is-a-3d-perlin-noise-function-used-to-generate-terrain