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.😜🤔😄

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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.