autoassimiler

A rare technical or administrative verb meaning for a group or system to assimilate itself into a larger one on its own initiative. Mostly found in sociology, linguistics, or organizational writing.

• La minorité s'est autoassimilée à la culture majoritaire. — The minority self-assimilated into the majority culture.
• Certains systèmes informatiques s'autoassimilent aux nouveaux formats. — Some computer systems self-assimilate to new formats.
• Ce phénomène d'autoassimilation reste peu étudié. — This self-assimilation phenomenon remains understudied.

This is a rare, specialist compound — don't reach for it in everyday conversation about someone adapting to a new culture; s'adapter or s'intégrer are the natural, common choices there.