The noise can be computed based on the Current Position or the Undisplaced Position (the position of the surface prior to displacement).
If you want your displacement and shading patterns to match, use the Undisplaced Position.
The number of noise layers used. More layers add successively more noise, creating a more detailed pattern.
Sets the lowest (starting) frequency of the noise layers.
The scaler used to determine the frequency of each sucessive layer of noise. Smaller numbers will cause the layers to be more closely spaced in frequency. Larger values will space them further apart.
The frequency exponent. This value is used to scale the magnitude of each sucessive layer of noise using the formula1/f^(3-2*Dimension); where f is the frequency of the noise being used for a given layer. It's called dimension since this value relates to the fractal dimension. Bigger values are rougher, smaller values are smoother.
The frequency exponent range. The frequency exponent specified by the dimension is itself offset as a function of the noise magnitude. This value adjusts that offset. This determines the so-called crossover scale of the fractal. 0 gives a uniform appearance. Negative values will smooth out the low valued areas, and positive values will smooth the high valued ones.
This value controls which particular variation of the appearance you get - without altering the qualities of the appearance determined by the other controls. So, for example, you can use this to animate the appearance by connecting this to Time, or create several unique instances of the appearance by setting this to different values.
The manifold over which to apply the noise. Defaults to P.