Noise Functions and Naming Conventions

For my noise functions, I like to use the names as published in the TMPA book mentioned below. However those names differs from the names given to the same functions in A:M. Let me digress for a moment about noise function naming conventions.

The first reference paper about the Use of Noise Functions that appeared in the 1985 SIGGRAPH Proceeding was "An Image Synthesizer" by Ken Perlin.

I will refer to this article as AIS.

The native noise functions available in A:M are derived from this article and the names given to them also are derived from their implementation in this article.

Parallel to that, where some very high level math books and articles about Fractals in general.

The main reference in this matter is "The Science of Fractal Images", H.-O. Peitgen & D Saupe Eds., Springer-Verlag, 1988. This book is filled with high level math that only a PhD in math could love.

I will refer to this book as SFI.

The reference first book concerned exclusively with noise functions and texturing was published in 1994: "Texture and Modeling, a Procedural Approach", D. S. Ebert Ed., Academic Press where you have authors F. Kenton Musgrave, Darwyn Peachey, Ken Perlin and Steven Worley. There currently is a second edition and I heard there is a third edition coming soon.

I will refer to this book as TMPA.

So not surprisingly, a lot of noise functions have names which do not concur with the names used in the TMPA book mentioned above. But since this book is now available as reference, I thought of bringing those clarifications.

The A:M Fractal Sum algorithm is described in the AIS article but is not given a name. And by the way, Ken Perlin uses the word "Octave" in this article to talk about the iteration in the fractalization loop although he doesn't mention the word fractal in his article. It is actually a sum of fractalized Perlin noise function. In the TMPA book, this is called FractalSum but later it is formalized as a fBM.

fBM stands for Fractal Brownian Motion. The fBM notion itself is formally defined in the SFI book but only really understandable to a Math wiz. This Brownian Motion is actually a theoretical model that defines the Fractal Dimension. In the Fractal study field, this BM covers much more than what we do with it in procedural texturing.

So the A:M fBM is, in the strictest sense of the word an fBM. But since the fBM notion covers so large, we could say that all A:M noise based combiners are fBMs. However, if we refer to the TMPA book, the A:M fBM is called VL fBM for Variable Lacunarity fBM. This in itself is a strange name because the procedure used to produce the function have little relation to lacunarity variation. It consist of perturbing the basic Noise function.

The A:M Perlin is described in the AIS article as a way to produce turbulence. It folds the values of the Noise function at half its value range and scale the result to cover the whole 0 to 1 range. This process introduces sharp changes in the texture pattern which are visible in those running lines. In the TMPA book, this folding technique is first called "turbulence" but is later used differently and called "ridged multifractal".

The A:M Sine is also described in the AIS article as a way to produce marble in combination with the turbulence function. It consists of transforming the values of the noise function through a sine wave.

The alternative implementation of the Perlin and Sine I provide are named Fractal Perlin and Fractal Sine because the folding and the sine transformation is applied to the result of the fractal sum while the A:M implementation applies the folding and the sine transformation before fractilizing them.

The other names I use are taken from the TMPA book. Those are Hetero, Hybrid and Ridged multifractals. Those functions are classical ones and are found only in the TMPA book.