The suffix -iĝ· has slightly different meanings, depending on the type of the word to which it's being appended. Using it instead of a passive phrasing (Maria naskis Jesuon en Betlehemo. → Jesuo naskiĝis en Betlehemo.) is only one of its purposes.
Some uses of the suffix -iĝ·
-iĝ· appended to a property-word (usually an adjective) produces a verb that indicates that the subject receives that property:
- pala (pale) → paliĝi (turn pale)
-iĝ· appended to an intransitive verb (a verb without direct object) means that the subject begins the corresponding action, or that the subject performs the action involuntarily.
- sidi (sit, = be in a seated position) → sidiĝi (sit, sit down = become seated, get into a seated position)
- morti (die) → mortiĝi (lose one's life)
-iĝ· appended to a transitive verb (a verb with a direct object) means that the subject does this action to itself or by itself, or that we don't care about the actual actor.
- La knabo turnis sian kapon. (The boy turned his head.) — La tero turniĝas ĉirkaŭ sia akso. (Earth turns around its axis. There's nothing/nobody turning the Earth, it turns by itself.)
fariĝi
fari is a transitive verb. (It usually has a direct object):
- Mi faras kukojn. — I make cakes.
- Oni faris lin generalo. (They made him a general.)
The sentence
La kuketoj fariĝis dum 20 minutoj.
would thus mean that the cookies somehow made themselves (or at least that it was as if they did so, i.e. they were very easy, quick and non-laborious to make, so that it didn't really matter who did that little work.)
Ŝi fariĝis kuracisto.
means that she made herself become a doctor. (Not that she forced herself, but that she worked towards becoming a doctor and succeeded. Think maybe of the term "self-made man".) In practice, it's used pretty much synonymous with just iĝi (become) (see PMEG).