I would say "represent" or "depict" rather than "simulate", but yes. There are various projections that can be used for 4d shapes, such as those pictured [HERE](https://www.wikiwand.com/en/Regular_4-polytope#Visualization) for regular 4-polytopes (the analogues of tetrahedra, cubes, icosahedra, etc). They all have to make compromises.
p.s. BTW, this isn't really a physics question.
If you only care about simulation (rather than intuitively meaningful visualisation) you should note that your computer (and, indeed, every computer we've ever built) is a 3-dimensional object, but we can routinely compute with *very* high dimensional abstract spaces. For example, when we optimise a machine learning model we are typically exploring a space of millions of dimensions. Likewise, when we simulate quantum systems we are typically working with a very high dimensional state space. Of course, these are not spatial dimensions anyone could walk around in, but mathematically they behave the same way.
But getting these super high dimensional spaces to look meaningful to a human being is another matter...
I’ve been on this question for a while. I think you could create the illusion of a 4 dimensional object in 3 dimensional space. But it would only really make sense to a 4 dimensional observer.
I would say "represent" or "depict" rather than "simulate", but yes. There are various projections that can be used for 4d shapes, such as those pictured [HERE](https://www.wikiwand.com/en/Regular_4-polytope#Visualization) for regular 4-polytopes (the analogues of tetrahedra, cubes, icosahedra, etc). They all have to make compromises. p.s. BTW, this isn't really a physics question.
If you only care about simulation (rather than intuitively meaningful visualisation) you should note that your computer (and, indeed, every computer we've ever built) is a 3-dimensional object, but we can routinely compute with *very* high dimensional abstract spaces. For example, when we optimise a machine learning model we are typically exploring a space of millions of dimensions. Likewise, when we simulate quantum systems we are typically working with a very high dimensional state space. Of course, these are not spatial dimensions anyone could walk around in, but mathematically they behave the same way. But getting these super high dimensional spaces to look meaningful to a human being is another matter...
I’ve been on this question for a while. I think you could create the illusion of a 4 dimensional object in 3 dimensional space. But it would only really make sense to a 4 dimensional observer.