The dignified way to describe the problem at hand is alluding to Brouwer's fixed-point theorem[1], with white noise as the fixed point.
The more practical way is alluding to The Human Centipede[2].
Either way, the feed-back loop doesn't result in a good output.
[1] https://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem
[2] https://en.wikipedia.org/wiki/The_Human_Centipede_(First_Seq...