Wolfram is kind of obsessed with cellular automata, even went and wrote a whole book about them titled "A New Kind of Science". The reception to it was a bit mixed. CA are Turing-complete, so yeah, you can compute anything with them, I'm just not sure that in itself leads to any greater Revealed Truths. Does make for some fun visualizations though.
The question really ultimately resolves to whether the universe can be quantized at all levels or whether it is analog. If it is quantized I demand my 5 minutes with god, because I would see that as proof of all of this being a simulation. My lack of belief in such a being makes me hope that it is analog.
A new kind of science is one of my favorite books, I read the entirety of the book during a dreadful vacation when I was 19 or 20 on an iPod touch.
It goes much beyond just cellular automata, the thousand pages or so all seem to drive down the same few points:
- "I, Stephen Wolfram, am an unprecedented genius" (not my favorite part of the book) - Simple rules lead to complexity when iterated upon - The invention of field of computation is as big and important of an invention as the field of mathematics
The last one is less explicit, but it's what I took away from it. Computation is of course part of mathematics, but it is a kind of "live" mathematics. Executable mathematics.
Super cool book and absolutely worth reading if you're into this kind of thing.