At the end of previus chapter we were thinking on noise as random smooth waves. This *wavely* nature of noise is what makes it such an interdisciplinary concept. In fact, in acustics, sound is constructed by the manipulation of the amplitud and frecuency of a sine waves.
At the end of the previous chapter we were thinking about noise and discovering that in fact noise could be interpreted as audio signals. In fact sound can be constructed by the manipulation of the amplitud and frequency of a sine waves.
```glsl
y = amplitud + sin( frequency );
```
An interesting property of waves is that they can be add up. The following graph shows what happen if you add sine waves of different frequencies and amplituds.
An interesting property of waves in general is that they can be add up. The following graph shows what happen if you add sine waves of different frequencies and amplitudes.
<divclass="simpleFunction"data="
float t = 0.01*(-u_time*130.0);
@ -17,9 +17,11 @@ y += sin(x*3.1122+ t*4.269)*2.5;
y *= 0.1;
"></div>
Think on the surface of the ocean. Massive amount of water propagating waves across it surface. Waves of diferent amplitud and frequencies coliding together.
Think on it as the surface of the ocean. Massive amount of water propagating waves across it surface. Waves of different heights (amplitud) and rhythms (frequencies) bouncing and interfering each other.
On other side if those sine waves are harmonics produce interesting patterns. Try the following code on the previus graph. As you can see in each iteration the frequency increase, while the amplitud decrese.
Musicians learn long time ago that there are sounds that play well with each other. Those sound, carried by waves of air, vibrate in such a particular way that the resultan sound seams to be bust and enhance. Those sounds are call [harmonics](http://en.wikipedia.org/wiki/Harmonic).
Back to code, we can add harmonics together and see how the resultant looks like. Try the following code on the previous graph.
```glsl
y = 0.;
@ -29,11 +31,15 @@ for( int i = 0; i < 5; ++i) {
y *= 0.6;
```
As you can see in the above code, on every iteration the frequency increase by the double. By augmenting the number of iterations (chaining the 5 for a 10, a 20 or 50) the wave tends to break into smaller fractions, with more details and sharper fluctuations.
## Fractal Brownian Motion
By adding different octaves of increasing frequencies and decreasing amplitudes of noise we can gain some extra granularity. This technique is call Fractal Brownian Motion and is very well documented in [this](http://www.iquilezles.org/www/articles/warp/warp.htm) [two](http://www.iquilezles.org/www/articles/morenoise/morenoise.htm) articles of Iñigo Quilez.
So we try adding different waves together, and the result was chaotic, we add up harmonic waves and the result was a consistent fractal pattern. We can use the best of both worlds and add up harmonic noise waves to exacerbate a noise pattern.
Take a look to the following example and progresively change the for loop to do 2,3,4,5,6,7 and 8 iterations. See how incrisinly fragmented this wave function becomes.
By adding different octaves of increasing frequencies and decreasing amplitudes of noise we can obtain a bigger level of detail or granularity. This technique is call Fractal Brownian Motion and usually consist on a fractal sum of noise functions.
Take a look to the following example and progressively change the for loop to do 2,3,4,5,6,7 and 8 iterations. See want happens
<divclass="simpleFunction"data="
float a = 0.5;
@ -43,19 +49,16 @@ for( int i = 0; i < 1; ++i) {
a *= 0.5;
}"></div>
If we apply this to 2D will look like the following code:
If we apply this one dimensional example to a bidimentional space it will look like the following example:
In this [article](http://www.iquilezles.org/www/articles/warp/warp.htm) Iñigo Quilez describe an interesting use of fractal brownian motion constructing patterns by adding successive results of fractal brownian motions.
Patricio Gonzalez Vivo
10 years ago