I'm not involved in this project, but I partially replicated the results from Mordvintsev et al. a few years ago because I found the idea interesting. The key idea for me was learning the possibly unknown rules of a CA from training examples. This sounded to me like something that could be useful in science, to learn about spatially distributed processes. Or in ML as a new idea for image classification or segmentation. The hope was always that a CA could be learned which would have a simple discrete representation which could then be used in inference with much lower computational needs than a full neural net. But unfortunately we never managed to succeed here, and I have the impression that this area is not as active anymore as it was some years ago.

I suppose the idea of this project is the same: show the correspondence between both in order to understand them better.

Anyway, some interesting papers from back then:

Cellular automata as convolutional neural networks: http://arxiv.org/abs/1809.02942

Image segmentation via Cellular Automata: http://arxiv.org/abs/2008.04965

It's Hard for Neural Networks To Learn the Game of Life: http://arxiv.org/abs/2009.01398

CNNs are CA if you don't insert fully connected layers, actually.

it has the signature style of an app generated from the claude web ui. There isn’t necessarily an it to get.

Any non-trivial property on CA is undecidable in any dimensions, IIRC you resort to Medvedev reducibility, oracles, etc... pretty quick with them.

IMHO this is semi interesting because having ANNs predict the outcome of deterministic dynamical systems may help with some planning tasks.