This operator generates 1D and 3D Perlin Flow noise from 3D and 4D data. There are two forms of Perlin flow noise: a non-periodic noise which changes randomly throughout the N-dimensional space, and a periodic form which repeats itself over a given range of the space. The periodic form can be used to generate patterns which 'tile' over N-dimensional space (i.e. a noise-based texture map which repeats seamlessly).
The noise has a range of (0, 1) with a median value of 0.5. The distribution of the noise depends on the dimension, with higher dimensions approaching a Gaussian distribution of noise values.
Flow noise is very similar to Perlin noise, as in Periodic Noise, but with an extra flow parameter. The flow parameter can be thought of as an extra dimension, but a dimension whose period is always 1. Moving through the flow dimension rotates the noise vectors rather than adjusts slices through a noise space; however, so generates a more flowing appearance to the animation, and hence the name.
This operator is just the building block noise, for higher levels consult the Anti-Aliased Flow Noise which performs multiple iterations.