Here is a cool project by Henry Segerman which involves applying the Droste Effect to spherical 360 videos. You can produce some trippy videos with this approach. As he explains, this was made using Möbius transformations, applied to video recorded by a Ricoh Theta S.
Spherical video editing with Möbius transformations
Spherical Droste video
You can find out more technical details about this project here.
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