''Print Gallery'' () is a

lithograph Lithography () is a planographic method of printing originally based on the miscibility, immiscibility of oil and water. The printing is from a stone (lithographic limestone) or a metal plate with a smooth surface. It was invented in 1796 by ...

printed in 1956 by the Dutch artist

M. C. Escher Maurits Cornelis Escher (; ; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made woodcuts, lithography, lithographs, and mezzotints, many of which were Mathematics and art, inspired by mathematics. Despite wide popular int ...

. 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 The Droste effect (), known in art as an example of ''mise en abyme'', is the effect of a picture recursion, recursively appearing within itself, in a place where a similar picture would realistically be expected to appear. This produces a loo ...

with visual

recursion Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in m ...

. The lithograph has attracted discussion in both mathematical and artistic contexts. Escher considered ''Print Gallery'' to be among the best of his works.

Origins

Bruno Ernst cites

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 Ballantine Books is a major American book publisher that is a subsidiary of German media conglomerate Bertelsmann. Ballantine was founded in 1952 by Ian Ballantine with his wife, Betty Ballantine. Ballantine was acquired by Random House in ...

, 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

In his book ''

Gödel, Escher, Bach ''Gödel, Escher, Bach: an Eternal Golden Braid'' (abbreviated as ''GEB'') is a 1979 nonfiction book by American cognitive scientist Douglas Hofstadter. By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Esc ...

'',

Douglas Hofstadter Douglas Richard Hofstadter (born 15 February 1945) is an American cognitive and computer scientist whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, Strange loop, strange ...

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").

Possible 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 Hendrik Willem Lenstra Jr. (born 16 April 1949, Zaandam) is a Dutch mathematician. Biography Lenstra received his doctorate from the University of Amsterdam in 1977 and became a professor there in 1978. In 1987, he was appointed to the faculty o ...

, reported a way of filling in the void by treating the work as drawn on an

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If the ...

over the field of

complex numbers In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a ...

. 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. Their website further explores the mathematical structure of the picture.

Post-modernism

''Print Gallery'' has been discussed in relation to

post-modernism Postmodernism encompasses a variety of artistic, cultural, and philosophical movements that claim to mark a break from modernism. They have in common the conviction that it is no longer possible to rely upon previous ways of depicting the wor ...

by a number of writers, including Silvio Gaggi, Barbara Freedman, Stephen Bretzius, and

Marie-Laure Ryan Marie-Laure Ryan is an independent literary scholar and critic. She has written several books and articles on narratology, fiction, and cyberculture and has been awarded several times for her work. She attended the University of Geneva to study li ...

References

External links

*
Artful Mathematics: The Heritage of M. C. Escher
by Bart de Smit and

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.
An Animation of ''Print Gallery''
created in Cindy JS {{Mathematical art Works by M. C. Escher 1956 prints