Neural cellular automata are interesting because they shift learning from “predict tokens” to “model state evolution.” That feels much closer to a transition-based view of systems, where structure emerges from repeated local updates (transitions) rather than being encoded explicitly.

I'm working on a theoretical/computational framework, the Functional Universe, intended for modeling physical reality as functional state evolution. i would say it could be used to replicate your CA process. Won't link it here to signal my good faith discussing this issue - it's on my GH.

“The long-term vision is: foundation models that acquire reasoning from fully synthetic data, then learn semantics from a small, curated corpus of natural language. This would help us build models that reason without inheriting human biases from inception.”

Reminds me of "Universal pre-training by iterated random computation" https://arxiv.org/pdf/2506.20057, with bit less formal approach.

I wonder if there is a closed-form solution for those kinds of initialization methods (call them pre-training if you wish). A solution that would allow attention heads to detect a variety of diverse patterns, yet more structured than random init.