Comment by pierrec
6 hours ago
This kind of technique can be used in 3D space as well! The analysis here represents Escher's techniques as conformal maps in the complex plane. Conformal maps are also possible, though more limited, in R^3. This is something that I explored some years ago and wrote an article about it, though it focuses more on graphics than math: https://www.osar.fr/notes/logspherical/
So to do this same Droste effect in 3D you would need a self-similar volume? Though since we can't really see 3D, we could never have that "one circle zooms in" effect.
Or could you walk around in such a world? That would be a very cool concept for a game.
Though since we can't really see 3D, we could never have that "one circle zooms in" effect.
Well, the 3D structure just needs to be sufficiently "holey" for the effect to become apparent. For example a cage-like structure, or a house with no roof (when seen from above).