Most discussion here is about the dirtier noise on your attached picture, but the link you posted - the blue and white noise - is a lot of crisp shapes.
For any sort of effect where you want to create a large number of slightly different shapes, a cool tool, is Illustrator's 'Scale Each' function.
First you'll need to cover a large area with the same shape using cut and paste , or duplicate etc.
This 'Scale Each ' command normally allows you to scale or rotate a number of items all by the same amount, but it has a little checkbox named 'random' allowing you to start with, say, 100 identical triangles in a grid but randomly move, size and rotate each of them all at once to create very chaotic patterns.
When you combine this with a distorting filter in Illustrator, like 'punk', you start to get the noisy yet clean shard shapes in your weblink.