In another discipline - maps - we are talking projections. Personally I would like a globe of the illuminated variety with a paper cylinder around it getting a Mercator projection on it.
Either way, the maths and software for this has been on the desktop for at least 25 years (render times were a while back then).
A central cylindrical projection is what you get when you put a light in the center of a sphere and project that on a cylinder
You could get pretty close with Braun type stereographical for non-global uses with a fixed light source.
Dot stereograms might be hard as it would be difficult to get fine dots. But in principle it should be possible to project stereograms. That would be one perverse pun on 3D.
(And a tiny nit-pick: Banksy didn't make the panda!)