Consider the task of generating random pretty images like the Electric Sheep project, but on the surface of a sphere. Enjoy the presentation on a spherical display, or with virtual reality from the inside of the sphere.
With virtual reality one can also add depth, perhaps wisps of colored translucent gas or kaleidoscopic polyhedra flying around.
There remains the details of encoding images and video for the surface of a sphere, though astronomers have already solved this with HEALPix.
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