One who or that which animates; a person or thing that gives life, movement, or spirit to something.
From animate + -er (agent noun suffix from Old English -ere). The -er suffix, one of the oldest and most productive in English, creates nouns indicating the doer of an action or the agent of a process.
While 'animator' is the standard modern form, 'animater' appeared in older texts and shows how English pronunciation influenced spelling—the -er vs -or distinction has always been somewhat flexible, and regional accents still affect which we prefer.
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