I'm just starting to get the hang of Perlin Noise in general, but many sites I've read up on in regards to terrain generation refer to a falloff value.
It seems quite typical in 3D (cube-based terrain) to use the result of a 3D Perlin Noise function as a density test, where if it's greater than 0 it's land, less than or equal to 0 is air. Then simply offset the result from the function by the current y value before you do the density test to get smooth semi-flat terrain.
What I don't understand is what is meant in regards to a falloff value.
Can someone please explain what a falloff value in this sense is referring to, perhaps even using a code example?
The falloff is used to determine the weight of the octaves. You can either use explicit weights, which allows you to customize the result in a wider variety. Or you can use implicit weights with a falloff value. This will set the weights to an exponential function.
E.g. if you have a falloff value of 0.5, then the octaves' weights are as follows (unnormalized)
Octave 1: 1 = falloff ^ 0
Octave 2: 1 * 0.5 = 0.5 = falloff ^ 1
Octave 3: 0.5 * 0.5 = 0.25 = falloff ^ 2
Octave 4: 0.25 * 0.5 = 0.125 = falloff ^ 3
The overall result is calculated with
Sum [i] ( (value of octave i) * (weight i) )
Typically a normalization is needed, so that weights sum up to 1.