How is a 3d perlin noise function used to generate terrain?

Question

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?

Answer 1

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.