Yep, see my comment above and especially http://arxiv.org/abs/1809.02942

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