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More sensible would be to project a 4-Dimensional object into a 3-Dimensional one, like a hologram. It would then only require the 3D slices to be shown in sequence, and viola! 4D TV.
Then, if it physically appears 3D, and we know that 3D can be represented on a 2D format, then it only remains to render a 3D cross-section onto a 2D screen, and then show the sequence of fourth-dimensional images strung together.
And there you have it. Disney/Pixar's Toy Story.
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No. It is easier to do it in one hit. I can handle 3D surface volumes of 4D Hyperspheres.
BTW, here's a bit of plot synopsis.
Humans, in the future, discover how to travel in 4-space. They go looking for other membranes to colonise, and soon find many small membranes. On one of these, they find some silicon-based lifeforms, that they then have skirmishes with. In one of these, a command center is lost, which contains details of hyperspatial technology. The silicon-based creatures immediately start spreading and attacking the humans. Later some totally biological creatures arrive and reveal that the silicon-based ones were exiles from them, but have now escaped their prison...