I just read the Wikipedia article on Rule 110 and there was a short remark that the simplicity of that rule might imply that it can exist in physical systems in nature. "Physical systems may also be capable of universality— meaning that many of their properties will be undecidable, and not amenable to closed-form mathematical solutions." I have two questions:
On which scales could such a system occur? Could parts of our brains be turing complete? Could movements of stars and galaxies follow simple rules like that?
What kind of properties wouldn’t we be able to decide and what would be the implications of it?
As Ben Crowell points out, any physical implementation of a Turing machine in a finite universe can only be an approximation because a Turing machine is defined as having infinite memory. And it is also true that a finite approximation to a Turing machine often behaves just like a Turing machine. But there's one difference that is important to your questions. On a finite approximation to a Turing machine the halting problem is decidable. That means that the presence of a rule 110 system (or any other Turing complete system) in a finite universe would not imply the existence of undecidable properties.