I imagine it would have to be some sort of impractically large closed-loop steam system, probably running around the perimeter of the pot, with a rotating paddle inside. Not at all practical, but it would be neat.
At a rolling boil you could probably get the pot stirring itself with surface geometry. Bubbles boil upwards, so putting the right fin shape should get it spinning. Seems like it would require a bunch of machine work so it would probably be prohibitively expensive to make.
This exists. I tried to find a link or video but it seems to have disappeared.
Edit: Here’s a page on it. It’s from 2012 though, I guess the idea never really took off.
https://newatlas.com/kuru-kuru-nabe-self-stirring-saucepan/22709/
I had a friend with a similar pot (might have been the same one shown there) and… oh my god, it was impossible to wash. Just awful. Neat to watch but oh man, never got used after that.
Why? It just looks like bumps, no? Did a sponge not get in there?
They’re pretty pronounced so there’s deep overhangs + not much working space on the interior. Fine to wipe down sure, but anything requiring even a little scrubbing was miserable and a standard dishwasher’s spray was blocked by the geometry. We tried to use it a couple times because it was neat but then everyone in the friend group collectively gave up on it as being very not worth it.
Is it this one? https://www.youtube.com/watch?v=91yoFz5XFqY
Looks like it!
You’ve got a bright future in crazy Victorian inventions if you can make a steam-powered time machine to get there.
That only makes me think of the inevitable outcome:

Best answer
With modern induction cooking this should not be as problematic. You can use the magnetic field to put something in motion
It’s called soup.
Then my soup isn’t working.
I think there is some chemistry equipment that does that?
hot plates have a motor and a magnet that couples with a stir bar.
there is however this sort of thing for stoves: https://www.amazon.com/JossaColar-Fireplace-Electric-Accessories-Thermometer/dp/B0BDM14HVM
That’s for a wood stove, to distribute heat throughout the home. While it might be possible to repurpose it, I don’t think it’s very practical



