“Random” pattern is pretty well what it sounds like. Because I’m a pedant I don’t like the name “random pattern” since it’s an oxymoron, but that’s just me.
The trick to get something interesting here is to simply make a flat laminate of as many layers as you want and make sure you deform it, do some stock removal, etc as you go along to reveal various layers in the pattern as you go. Many times, simply welding and drawing a billet will create a “random” effect if you don’t have very square press or hammer dies, or if you’re hand forging. This is due to the fact that you’re not deforming the billet during forging in a regular fashion, so you’re sort of pushing the layers all around as you work.
Here is an example of a “random” knife I made a while back.