“Are you really sure that a floor can’t also be a ceiling?” M. C. Escher

“Are you really sure that a floor can’t also be a ceiling?” M. C. Escher

Originally shared by Matthew Baggott

Animating the Mathematical Logic of M.C. Escher For his 1956 Prentententoonstelling (Print Gallery), M. C. Escher started with “the idea that it must…be possible to make an annular bulge,” “a cyclic expansion … without beginning or end.” He created a recursive drawing of a gallery displaying prints. One print in the gallery shows a seaport containing the original print gallery. He projected this image onto a cyclically expanding grid with curved lines folding inward.

A cool 2003 article in Notices of the AMS shows his original grid, an ‘unfolded’ version of the Escher drawing, and various permutations of the basic concept. As a companion to their 2003 article, B. de Smit and H. W. Lenstra have created a rad website and animations, one of which I have converted from AVi to GIF using VirtualDub for our viewing pleasure.

This picture-within-itself strange loop imagery is sometimes called mise en abyme or, more commonly, the Droste effect, after the recursive label on a brand of Dutch cocoa powder. Thanks to the mathematical exposition by de Smit and Lenstra, you can now find tutorials for creating your own images using programs like GIMP or Photoshop. A flickr group exists for such images.

article: http://www.ams.org/notices/200304/fea-escher.pdf

website: http://escherdroste.math.leidenuniv.nl/index.php?menu=intro

(h/t to Philip Smith for pointing me to the website)

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5 Responses to “Are you really sure that a floor can’t also be a ceiling?” M. C. Escher

  1. Reminds me of the line “spinning to infinity” in Call Me Al by Paul Simon. ~:-o

  2. Rajini Rao says:

    Lovely man, Paul Simon!

  3. Kapil Ranade says:

    Yeah. Escher’s engravings were superb. Small wonder that Hoffstadter finds them so useful to illustrate his theories of awareness as a ‘self referential loop’.

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