The song has been described as a "self-referential and infinitely iterative children's song". I would like to use a word that encapsulates this description.
I have considered recursive, but does that necessarily imply self-referentiality? I don't think it would imply an infinite process either.
Eternal or never-ending only describes one facet.
A quine may be apt, but does the analogy really hold? Again, a quine doesn't imply infinite reproduction, or does it? They output themselves only once in examples I've seen.
Is there any appropriate term (via linguistics, computer science, physics, etc.) that completely captures the essence of the song (and similar works)?
Edit: I'm also considering ouroboros. My goal is to find something that is descriptive or directly analogous to the underlying pattern. I'm not sure if there's some jargon in other fields, biology, music, art, etc. that could apply. The fact that it's a children's song is irrelevant, so I have emphasised the crux of the quoted phrase.