Möbius-Transforming Spherical Images

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Paper von Saul Schleimer und Henry Segerman (PDF) über Möbius-Transformationen und Droste-Pics. Von der Mathematik dahinter verstehe ich nicht allzuviel, aber ich liebe den Droste-Effekt und Rekursion. Die Pics im Paper stammen teilweise aus diesen Videos.

A common artistic and mathematical motif is that of “self-similarity”; this is often called the Droste effect in commercial and computer graphics. A “straight Droste effect”, as found on the packaging of the eponymous Dutch cocoa, is obtained when the entire picture is included, under a shrinking transformation, inside of itself. The “twisted Droste effect” was first introduced by M.C. Escher in his Print Gallery lithograph. The mathematics behind Escher’s image was explained by Bart de Smit and Hendrik Lenstra.

It is possible to obtain both the straight and twisted Droste effect in spherical images using Mobius transformations, the complex exponential map, and the complex logarithm (see also [10, page 223]). We simplify the discussion here by suppressing all mention of equirectangular and stereographic projections.

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