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3d noise turbulence functions for terrain generation

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For my masters thesis I am investigating methods to generate entire planets procedurally on the gpu.
I'm currently generating 33x33 size patches in compute shaders, and store height and normal data in a structured buffer.
I then render a single 33x33 grid using hardware instancing, by projecting it to its correct location and sampling the generated data from the structured buffer.
So far this is working very well, and it is easily fast enough to regenerate the entire geometry every frame.

Whilst this is sufficient for the thesis, using only fBm turbulence looks very boring, and not at all like actual terrain.
Unfortunately I'm having a very hard time coming up with decent turbulence functions to produce good results.

My current approach is to first generate a continent/ocean map, using 5 octaves of fBm turbulence, which produces something like this:

This is not bad, I can work with that as a basis.
If I add climate zones to that (equator gets more sand like textures, and poles get snow at lower height levels...).
I should also be able to generate a mountain map using the same technique with only a few octaves of noise.

But I'm at a loss as to how to generate the close up geometry.
I can't figure out how to generate any decent looking mountains at all, which are probably the most important feature.
I've experimented with ridged multifractals a lot, but this is the best I can come up with:

For which I've used the following turbulence function:
float rnoise(float3 p)
float n = 1.0f - abs(inoise(p) * 2.0);
return n*n - 0.5;
float rmf(float3 p, int octaves, float frequency, float lacunarity, float gain)
float sum = 0;
float amp = 1.0;
for(int i = 0; i < octaves; i++)
float n = rnoise(p * frequency);
sum += n * amp;
frequency *= lacunarity;
amp *= gain;
return sum;

With the parameters
float Height = pow(2.0, rmf(p, 18, 300.0, 1.75, 0.6));

And this looks pretty bad.
The placeholder textures aren't helping either, but that's another issue.
I don't really know where to go from here.
The only turbulence functions I can find are fBm and ridged multifractals.

The exception being Gilliam de Carpentier, who has a few really cool examples of using noise derivatives on his blog:

Unfortunately I get very different results with the same techniques, which I'm assuming is because he's using 2d noise and I'm using 3d noise.

I don't really know where to go from here.
Clearly I need different turbulence functions, but I don't know where to find, or how to discover new ones.
I appreciate any suggestions on the matter.


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Some sort of RidgedMultifractal noise function may help here. 



The guys that built libnoise may have some sample code you can use written in c++ ... shouldn't be too hard for you to convert to shader code I would think (it's purely logic after all).




I also built a basic tool for messing with this on a web page ...




It's not perfect but hey it only took me a few hours, but at least it could help you visualise the noise function results to see if they will fit what you need before you go writing tons of code.


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I've played with noise a lot in the past, and the simple fact is that there are limitations to what these simple, elegant little functions can do. You can implement module chaining, ala the libnoise Select and Blend functions, to vary the terrain types from among the common functions. You can implement F2-F1 cellular noise to approximate "chunky" mountains. You can apply domain perturbations to alter the character of the basic functions. But ultimately, without analogues to physical processes such as hydraulic and thermal erosion, uplift, folding, tectonics, etc... you're going to be unable to achieve some of the more interesting results on display in the real world. There really is only so much a f(x,y,z) can really do.


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