You can have C without relativity. There are no relative reference frames in GoL. Reactions only work at specific absolute speeds, and most of them only work at absolute speed 0.

Relativity can exist in an absolute environment like GoL if you consider the momentum of the quantum vacuum virtual particles. Look it up :-)

Seriously guys. Downvotes for talking about digital physics? Sad me.

https://en.wikipedia.org/wiki/Superfluid_vacuum_theory#Relat...

"Relativistic quantum field theory"

Downvotes for asking whether we're certain of some rather ignorant assumptions. -4 for me.

Um, my first comment was just referring to the fact that in an absolutely framed turing-complete environment. One can sprout a quantum vacuum full of constant noise, ie. constant producing and annihilating structures(analagous to virtual particles.)

This is already experimentally observed in our own universe. Quantum noise exists in vacuums.

If you look at C in GoL as the fastest an actual black square can propagate, then of course you'll validate your naive assumptions that our universe could never be digitally replicated by GoL. But if you take the idea of implementing a primordial sea of quantum noise, and looking at the GoL board not as physical particles directly, but as a deeper construct. Then you can actually replicate relativity.

http://arxiv.org/pdf/physics/9902034.pdf