In a manner relating to or based on someone's own life story; in a way that describes personal experiences.
From autobiographic + -ally (forming adverbs). This adverbial form appeared as autobiography became more established as a literary genre in the 19th and 20th centuries.
When authors write 'autobiographically,' they're blending the intimate perspective of personal experience with the craft of storytelling—it's why some novels feel so true even when they're entirely fiction.
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