Noise tends to means different things for different people. Musicians will think it in disturbing sounds, communicators as interference and astrophysics as cosmic microwave background. In fact most of this concept have one things in common that bring as back to the begining of random. Waves and their properties. Audio or electromagnetical waves, fluctuation overtime of a signal. That change happens in amplitud and frequency. The ecuation for it looks like this:
By doing the last to excersize you have manage to "modulate" a sine wave, and you just create AM (amplitud modulated) and FM (frequency modulated) waves. Congratulations!
Another interesting property of waves is their ability to add up. Comment/uncomment and tweak the following lines. Pay atention on how the frequencies and amplitudes change conform we add different waves.
By adding different iterations of noise (*octaves*), where in each one increment the frequencies (*Lacunarity*) and decreasing amplitude (*gain*) of the **noise** we can obtain a bigger level of granularity on the noise. This technique is call Fractal Brownian Motion (*fBM*) and in it simplest form looks like the following code
This techniques is use commonly to construct procedural landscapes. The self similarity of the fBm is perfect for mountains. If you are interested in this use you defenetly should read [this great article of Inigo Quiles about advance noise](http://www.iquilezles.org/www/articles/morenoise/morenoise.htm).
![Blackout - Dan Holdsworth (2010)](holdsworth.jpg)
Using escentially the same technique is also possible to obtain other effect like what is known as **turbulence**. It's esentially a fBm but constructed from the absolute value of a signed noise.
[Inigo Quiles wrote this other fascinating article](http://www.iquilezles.org/www/articles/warp/warp.htm) about how is possible to use fBm to warp a space of a fBm. Mind blowing, Right? Is like the dream inside the dream of Inception.
![ f(p) = fbm( p + fbm( p + fbm( p ) ) ) - Inigo Quiles (2002)](quiles.jpg)
A mild example of this technique is the following code where the wrap is use to produce something this clouds-like texture. Note how the self similarity propertie still is apreciated.