I was doing something similar with fluid equations on meshes more than ten years ago. Once you have Automatic Differentiation it's fairly straightforward to reformulate a time evolution process into one that solves for some free parameter.

It's a pity they don't give a video of the butterfly battle, that sounds a lot more impressive than the static 2d lizard.

What I'd love to see is a reproduction of the kind of embryo development videos you can get from lightsheet microscopy, e.g. https://youtube.com/watch?v=2Vnyph3Vmic

You can probably manage to reproduce the butterfly battle here (original paper): https://distill.pub/2020/growing-ca