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Some of them don’t care about being remembered or how they’re remembered.
But some of them very much do:
https://www.rand.org/pubs/commentary/2023/07/when-mass-shooters-are-seeking-fame.html
https://www.sciencedirect.com/science/article/abs/pii/S1359178916300027
Example:
https://www.desmoinesregister.com/story/news/crime-and-courts/2024/10/18/perry-school-shooting-suspect-dylan-butler-wanted-to-gain-notoriety-police-say/75733220007/