The Octave and other noise parameters

In order to defeat the underlying grid regularity and the smoothness of the noise function, we will fractalize it. This means that we will overlay smaller and smaller copies of the same noise functions over the previous layers in order to add details.

Technically, this is called Spectral Synthesis.

So, Given the basic noise function displayed beside, fractalizing it will produce this.

The first layer is the basic function with reduced contrast. The second layer is the same noise function but at 1/2 scale the original and half the contrast as the first layer. Then the third layer is yet again the same function but scaled 1/2 of the previous one (so actually 1/4 scale the original) and half the contrast as the previous layer. When the 3 layers are added together, it produces the resulting noise function at the right, above.

The Octave property is the number of layers that are added together. Each time a new layer is added, it is scales 1/2 the previous layer and the contrast is also reduced half the previous layer.

At Octave = 1, only the basic noise pattern is used. At Octave = 2, a 1/2 scale noise pattern is overlayed on top of the basic pattern. And at Octave=3, the overlays are 1/4 scale over the 1/2 scale over the basic. You get the idea. The higher octave you set, the more details you add.

The Lacunarity

Before going on about Lacunarity and Fractal DImension, you may wonder why I talk about that since you can't find those properties in A:M turbulence combiners. That's because you will find them in my Musgrave combiner Plugin which you may download from my Downloads Page.

Lacunarity is the property that controls the relative scaling of each new layer. So because the scaling from one layer to the next is 1/2, the lacunarity of native A:M noise functions is set to 2. Setting the lacunarity to 3 means that each new layer is 1/3 the scale of the previous layer. A Lacunarity of 3 would give this:

A Lacunarity of 3 gives overlays of 1, 1/3 scale, 1/9 scale, 1/27 scale, etc.

At a Lacunarity of 3, you start seeing repeating patterns developing in the texture. That is because, there are missing octaves values. We skipped 1/2 octave in the detail patterns and at lacunarity = 4, we skipped a full octave in the patterns thus making the repeating patterns of the scaled down layers visible because the frequency space is not completely filled.

Decreasing the Lacunarity will have the inverse effect. Meaning that there will be overlaps in the octaves of the different details overlays. At Lacunarity = 1, you overlay details at the same scale as the original so you get the equivalent of the Octave = 1 pattern. At Lacunarity lower than 1, the overlays are scaled up instead of down which have the effect of enlarging the pattern which is not very useful.

Note that even though the relative scale from one layer to the previous one is now 1/3, the relative contrast is still 1/2.

The Fractal Dimension

The Fractal Dimension is the property that controls the relative contrast from one layer to the previous one. In the case of the Fractal Dimension, the relation is not so easy to understand but basically, a fractal dimension of 1 produces a relative contrast of 1/2. And the higher the fractal dimension, the lower the difference in contrast. In other words, increasing the Fractal dimension will increase the contribution of the smaller scale layers thus increasing the details in the noise function. For example, with a Fractal Dimension of 2.2, a 3 Octave noise function will produce this:

A Fractal Dimension of 2.2 is what is normally used to generate terrains. So Fractal Dimension controls the sharpness of overlay details. Normally, the deeper we go into the detail overlays, the less contrast we have in the details. By increasing the fractal dimension, we increase the relative contrast of each successive overlay.