Print Gallery (M. C. Escher)
{{short description|Lithograph printed in 1956 by the Dutch artist M. C. Escher}}
{{italic title}}
File:Print Gallery by M. C. Escher.jpg, 1956]]
Print Gallery ({{Langx|nl|Prentententoonstelling}}) is a lithograph printed in 1956 by the Dutch artist M. C. Escher. It depicts a man in a gallery viewing a print of a seaport, and among the buildings in the seaport is the very gallery in which he is standing, making use of the Droste effect with visual recursion.{{cite web |last1=Merow |first1=Katharine |title=Escher and the Droste Effect |url=https://www.maa.org/meetings/calendar-events/escher-and-the-droste-effect |publisher=Mathematical Association of America |date=2013 |url-status=live |archive-url=https://web.archive.org/web/20130802065246/https://www.maa.org/meetings/calendar-events/escher-and-the-droste-effect |archive-date=2 August 2013}} The lithograph has attracted discussion in both mathematical and artistic contexts. Escher considered Print Gallery to be among the best of his works.Locher, J.L. The Magic of M.C. Escher. Harry N. Abrams, p. 133.
Origins
Bruno Ernst cites M. C. Escher as stating that he began Print Gallery "from the idea that it must be possible to make an annular bulge, a cyclic expansion ... without beginning or end."Ernst, Bruno. De toverspiegel van M. C. Escher, Meulenhoff, Amsterdam, 1976; English translation by John E. Brigham: The Magic Mirror of M. C. Escher, Ballantine Books, New York, 1976 Escher attempted to do this with straight lines, but intuitively switched to using curved lines which make the grid expand greatly as it rotates.
Seeming paradox
File:Escher Paradox Diagram.png in his 1980 book Gödel, Escher, Bach]]
{{further|Mathematics and art#Illustrating mathematics}}
In his book Gödel, Escher, Bach, Douglas Hofstadter explains the seeming paradox embodied in Print Gallery as a strange loop showing three kinds of "in-ness": the gallery is physically in the town ("inclusion"); the town is artistically in the picture ("depiction"); the picture is mentally in the person ("representation").{{cite web |last=Cooper |first=Jonathan |title=Art and Mathematics |url=http://www.doctordada.com/art/art-and-mathematics/ |access-date=5 September 2015 |date=5 September 2007}}
Possible Droste effect
{{further|Droste effect}}
Escher's signature is on a circular void in the center of the work. In 2003, two Dutch mathematicians, Bart de Smit and Hendrik Lenstra, reported a way of filling in the void by treating the work as drawn on an elliptic curve over the field of complex numbers. They deem an idealized version of Print Gallery to contain a copy of itself (the Droste effect), rotated clockwise by about 157.63 degrees and shrunk by a factor of about 22.58.{{Cite journal |last1=de Smit |first1=B. |last2=Lenstra |first2=H. W. |title=The Mathematical Structure of Escher's Print Gallery |year=2003 |journal=Notices of the American Mathematical Society |volume=50 |issue=4 |pages=446–451}} Their website further explores the mathematical structure of the picture.{{cite web |last1=Lenstra |first1=Hendrik |last2=De Smit |first2=Bart |title=Applying mathematics to Escher's Print Gallery |url=https://escherdroste.math.leidenuniv.nl/|publisher=Leiden University |archive-url=https://web.archive.org/web/20180606093355/https://escherdroste.math.leidenuniv.nl/ |access-date=6 June 2018|archive-date=2018-06-06 }}
Post-modernism
Print Gallery has been discussed in relation to post-modernism by a number of writers, including Silvio Gaggi,{{Cite book | first=Silvio | last=Gaggi | year=1989 | title=Modern/Postmodern: A Study in Twentieth-Century Arts and Ideas | publisher=University of Pennsylvania Press | isbn=0-8122-8154-3 | pages=44–45}} Barbara Freedman,{{Cite book | first=Barbara | last=Freedman | year=1991 | title=Staging the gaze: postmodernism, psychoanalysis, and Shakespearean comedy | publisher=Cornell University Press | isbn=0-8014-9737-X | pages=[https://archive.org/details/staginggazepostm00free/page/124 124–126] | url=https://archive.org/details/staginggazepostm00free/page/124 }} Stephen Bretzius,{{Cite book | first= Stephen | last=Bretzius | year=1997 | title=Shakespeare in theory: the postmodern academy and the early modern theater | publisher=University of Michigan Press | isbn=0-472-10853-0 | page=57}} and Marie-Laure Ryan.{{Cite book | first=Marie-Laure | last=Ryan | year=2000 | title=Narrative as virtual reality: immersion and interactivity in literature and electronic media | publisher=Johns Hopkins University Press | isbn=0-8018-6487-9 | page=165}}
References
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External links
- {{cite AV media |people=HarryCarry5 |date=Jul 26, 2009 |title=Escher's Print Gallery Explained |url=https://www.youtube.com/watch?v=wzfTzj2tiew |publisher=YouTube}}
- [https://www.ams.org/notices/200304/fea-escher.pdf Artful Mathematics: The Heritage of M. C. Escher], by Bart de Smit and Hendrik Lenstra
- [https://www.shadertoy.com/view/Mdf3zM Escher's prentententoonstelling] (Escher's picture gallery) shows an animation of the mathematical transformations involving a 3-D model of the town and art gallery, complete with source code.
- [https://cindyjs.org/gallery/main/Droste/ An Animation of Print Gallery] created in Cindy JS
{{M. C. Escher}}
{{Mathematical art}}