Sorry, it's too large... Stack overflow!😜

Practically yes, but theoretically?

If all you care about is some kind of local, visual representation at any one time, at a very non-detailed level; perhaps even possible "practically." But I'd need a far more detailed specification of your requirements.😜🤔😄

No I really mean the whole thing, electrons to galaxies, and I really do mean theoretically, is there anything in the universe that just isn’t “simulateable?”

So, if we stipulate that we have a thoroughly accurate understanding of all the components that make up the current universe--and I'll provisionally extend your characterization lower; to, quarks? superstrings? and, at the other end of the scale to the very large structures of multiple galaxies now observed that are tearing barn-sized holes in the "big bang" theory--Assuming our understanding is 100% true and correct, even then only a portion at a time... pieces and parts of the universe... could be simulated. Why? In order to accurately simulate the universe in its entirety would *require* an entity *outside* of the universe of adequate capacity to representationally simulate every detail of this universe including the instantaneous state of all of its content... Anything less would be a mere localized "holodeck" experience.

Imagine a function, let’s say “phi” , that generates conway’s games of life such that none of these games are periodic (repeat after any x generations) or become stable after some generations. If our universe is simulate-able then it must be a part of this set generated by such phi, since the set would contain all possible aperiodic games. Our own universes aperiodicity is ensured by the Second law of thermodynamics, since entropy always increases. Do I make sense?

I'm familiar with Conway's life; but the function you postulate sounds akin to the old "infinite number of monkeys would create Shakespeare's plays" gambit, and I'm not buying it.😜 So, no, I'm not following your train of thought, not without some further explanation, perhaps especially of where you're going with this?🧐