Word to describe an object in continuous cycle that is eventually ejected when it matures

I'm trying to find a word or phrase that best describes the process of an object or entity that enters a continuous cycle until it grows large enough or matures to a point of self-sustainability.

Example: A person who enters rehab for help on some problem and stays within the system until the person has matured or grown to some point (after undergoing repeated examinations) that the subject can once again enter society.

Example: A college paper that starts as a rough draft, submitted for review by a peer, and returned with improvements. This cycle is ongoing until the paper is (mostly) cleared of flaws by peers and the author, finally graduating to a final draft ready for submission (the ejection from the cycle)

Sounds like it would be called an iterative process. Or maybe a recursive one.

Because you say "cycle" and "grows larger...matures", I'll say, "maturation" - the process of developing

I would also go with Fortunate1 and say "evolution"

Evolving, at least as it involves a self-contained creative endeavour.