Any ordered dithering algorithm will animate pretty smoothly, but techniques based on error diffusion will have a "swimming" effect. Lucas Pope's devlog goes into considerable detail. Here's a good starting point: https://forums.tigsource.com/index.php?topic=40832.msg104520...
(ETA: also the link that gruez posted. HN seems to be having some performance issues)
I originally found out about Obra Dinn by reading that devlog—it's totally fascinating, and shows impressive attention to detail.
> It feels a little weird to put 100 hours into something that won't be noticed by its absence. Exactly no one will think, "man this dithering is stable as shit. total magic going on here."
Luckily, thanks to this post, we have the privilege of thinking that.
He's not entirely correct, either. I haven't played it, but I did see video of it, and I was impressed by the stability of the dithering. It takes work to avoid it looking like https://www.youtube.com/watch?v=2AKtp3XHn38 or something.