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At some point it was possible to play Doom as favicon.

Firefox only though, and doesn't work anymore.

https://vidferris.github.io/FaviconDoom/favicondoom.html

Still works here, using Firefox 84 on Ubuntu. That's pretty cool.

Looks like it uses JS to constantly update the favicon so it matches the DOOM screen.

I've seen a game there, Defender of the Favicon: http://www.p01.org/defender_of_the_favicon/

It's been possible for a long time to use canvas to generate an image that can be transferred into the favicon, essentially using javascript to create a dynamic/animated favicon.

You can already put CSS in an SVG favicon. That's one way to adapt a favicon to a user's native dark mode/light mode preference.