There are many places where fractal noise is useful in rendering. Taking this screenshot;
The mottled appearance of the distant meadow and the placing of the grass blades are controlled by a 3 sample fractal. Normally noise is added to a scene by building a Perlin or Simplex noise texture and sampling from it. However the repetition of this is easy to see and multi-sampling using offset coordinates is the only way to achieve this.
Using a Fractal noise function can be more efficient – not least becasue it doesn’t need a noise texture passed down into the GPU. There are quite a few examples out there for OpenGL and these are easy to convert into DirectX HLSL.
The one I used was https://github.com/ashima/webgl-noise which produces a Simplex noise, and call it with the sample Step 4 – Fractal Noise. Calling the noise function from the Fractal function gives you a good library. I wont post the original code here because these sites are worth visiting – there is more in there than just the noise functions.