Perlin Vs. Fractal Vs. Turbulent Noise

Question

I know what Perlin noise is (I wrote some code to generated it).

I believe fractal noise is scaled and summed Perlin noise, is that correct?

I sometimes see Turbulent noise and Perlin noise in the same article, but then the article does on to talk just about Perlin noise. How do they relate?

Answer 1

Perlin noise is a type of gradient noise generated via hashing coordinates to correspond to stochastic values (which are your gradient). This method then interpolates between the gradients to give a better resulting noise than value noise in which you merely interpolate between the values at each hashed integer coordinate.

when scaled one pixel to one integer coordinate, both gradient and value noise look indistinguishable from white noise. This changes when you introduce octaves. Instead of just generating the gradient or value at each point you scale your grid and sum the values several times (exactly like you stated). Fractal Noise is any noise which produces a fractal, octave noise summing produces Fractal Noise. This is because octaves introduce self similarity and other effects necesary for noise to be fractal.

While octave summing is by far the most popular technique to achieve fractal noise, fractal noise itself is not mutually exclusive from other types of noise. Perlin noise with octaves for example is Gradient Fractal Noise.

Turbulence means two things first:

Turbulence noise can be an additional modifier on a fractal noise which takes the absolute value of output in order to create valleys and end up looking like cloud turbulance. You can invert this to create ridges as well. You end up with images like this:

http://www.neilblevins.com/cg_education/procedural_noise/perlin_turb_max.jpg

It also refers to warping space of another texture for example what is described here towards the bottom. In as sense you ad turbulence to the image. This process uses the same hashed indexing as perlin and other methods use.

You can have gradient fractal turbulence noise, none are mutually exclusive.

Answer 2

I'm not sure what fractal noise is, but Perlin turbulence is the layering of perlin noise functions in order to give more detail and shape.

Each layer is called an octave and these layers are summed. Every layer has a finer density of lattice points compared to the previous layer. This means that general trends are dictated by the first, broadest layer, and subsequent layers add detail.

You mentioned an article on Noise and Turbulence and say it only talks about noise, I believe you are referring to http://paulbourke.net/texture_colour/perlin/ but even though Paul Bourke keeps using the word "noise" I'm under the impression that the examples describe turbulence.