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escher & the droste effect

One more on Escher... An old favorite site is 'Escher and the Droste effect', presenting a mathematical analysis of Escher's 'Print Gallery' ('Prentententoonstelling', 1956).

M.C. Escher - 'Print Gallery'

In 'Gödel, Escher, Bach', Douglas Hofstadter used this picture as an example of what he called 'strange loops', where two levels of reality interconnect in an endless circularity: the man in the picture gallery looking at a picture of a town with a picture gallery containing the man looking at the picture, and so forth ad infinitum.

But as Hofstadter realized, the picture also suggests another kind of loop, contained in the white patch in the middle, where Escher put his signature.

...Escher could not have completed that portion of the picture without being inconsistent with the rules by which he was drawing the picture. That center of the whorl is - and must be - incomplete. Escher could have made it arbitrarily small, but he could not have gotten rid of it.

What the team at Leiden University showed is that in the center the picture would endlessly repeat in smaller versions of itself. This is what in Dutch is called the Droste effect, after the famous Droste cocoa tin with the nurse carrying a tray with a cocoa tin with a nurse carrying a tray with a cocoa tin, and so forth ad infinitum again.

Thus 'Print Gallery' contains an infinitely recursive infinite loop. Its dizzying effect is best experienced in these animations.

See also this NY Times article.


escher's metamorphoses

What I didn't know: there are three different versions of M.C. Escher 's wall-covering woodcut 'Metamorphosis'. Interesting to see the development of this work, which seems to combine all Escher's creativity and tesselation genius in o… Read the full post »

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