Fractal noise (fBm)

Last lesson you added three layers by hand. Fractal noise (fBm) is the same thing written as a loop, so you can have any number of layers without copy and paste. Every time round the loop:

• add this layer: v += amp * vnoise(p)
• make the next layer twice as detailed: p = p * 2.0 + offset
• make the next layer half as strong: amp *= 0.5

Loops are allowed in shaders when they have a small fixed count; each pixel runs the loop on its own.

float fbm(float2 p)         // needs hash() and vnoise() declared above it
{
    float v = 0.0;           // the running total
    float amp = 0.5;         // strength of the current layer
    for (int i = 0; i < 5; i++)
    {
        v += amp * vnoise(p);                 // add this layer
        p = p * 2.0 + float2(13.7, 7.1);      // twice as detailed (and a new offset)
        amp *= 0.5;                           // half as strong
    }
    return v;
}

This is the most useful building block for natural effects (clouds, fire, terrain). You will use it in the arcade.