''Print Gallery'' () is a lithograph printed in 1956 by the

Dutch Dutch commonly refers to: * Something of, from, or related to the Netherlands * Dutch people () * Dutch language () Dutch may also refer to: Places * Dutch, West Virginia, a community in the United States * Pennsylvania Dutch Country People E ...

artist

M. C. Escher Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for most of his life neglected in t ...

. 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 Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathemati ...

. 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, 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'', 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").

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 ...

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 ...

. 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 is an intellectual stance or mode of discourseNuyen, A.T., 1992. The Role of Rhetorical Devices in Postmodernist Discourse. Philosophy & Rhetoric, pp.183–194. characterized by skepticism toward the " grand narratives" of modern ...

by a number of writers, including Silvio Gaggi, Barbara Freedman, Stephen Bretzius, and Marie-Laure Ryan.

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