Every time a number between 0 and 1 is multiplied by itself, it gets smaller. And the smaller the number is to begin with, the smaller it gets. This also means that numbers closer to 1 don't get reduced that much. By multiplying it by itself 4000 times, most of the noise gets nearly inaudible and only a few peaks remain, which become the crackles. 4000 just seemed to be about when it started to sound like a record crackling to me. It's probably worth playing around with that number. Actually, it probably makes more sense to make it an odd number to keep it biased around DC (even powers result in negative input giving positive output).