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to be scorched into; to be seared into
to make a strong impression; to be etched in (one's memory)
あの夕焼けの色が瞼に焼き付いた。
Those sunset colors burned themselves into my mind.
あの事故の光景は今も脳裏に焼き付いている。
The scene of that accident is still seared into my memory.
子供の頃に見た景色は心に焼き付く。
Scenery seen in childhood burns itself into the heart.