Print Gallery
Print Gallery (Dutch: 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. The lithograph has attracted discussion in both mathematical and artistic contexts. Escher considered Print Gallery to be among the best of his works. [5]
Escher’s lithograph contained a void blurry spot with his signature in the middle of the image. In 2002 the Dutch mathematicians Hendrik Lenstra and Bart de Smit investigated the question how the spot in the middle could reasonably be filled. They found very interesting connections to the complex exponential, and doubly periodic functions, and related it to the so called “Droste Effect” of self referencing images containing themselves as part. Their reconstruction allowed, depending on a complex integer parameter, to create other variations with the same artistic content but different geometry.
Grant Sanderson (3Blue1Brown) produced the following video explaining the underlying mathematical concepts behind this image.
References
Génard, André. 2008. Mathematics, Music, Art, Architecture, Culture. pp. 449-452. Tarquin Publications. http://archive.bridgesmathart.org/2008/bridges2008-449.html.
The blank, circular area in the centre of the lithography ‘Print Gallery’ (‘Prentententoonstelling’ 1956), by M.C. Escher (1898-1972) was examined and ‘filled in’ in the year 2000. This was done simply by reconstructing the circumstances in which the print was created, and in particular by picking up the drawing process where Escher had stopped. Of course, the question remains whether Escher had ever intended to ‘fill in’ that blank, circular area.
“Print Gallery (M. C. Escher).” Wikipedia, July 23, 2026. https://en.wikipedia.org/wiki/Print_Gallery_(M._C._Escher).
[ ℰ ] “Print Gallery Explained: The Infinite Loop Hidden in the Image — EscherExplained.com.” EscherExplained.com. Accessed August 19, 2026. https://www.escherexplained.com/print-gallery.
[ ℰ ] Richter-Gebert, Jürgen. “Math Visuals.” Math Visuals, 2026. https://mathvisuals.org/PrintGallery/.
Visit this site if you want to play with this concept interactively. The animation is based on Lenstras and de Smits work and their reconstruction of Escher’s Print Gallery. Moving the “zoom” slider allows spiraling and zooming into the image to see its contents in various magnifications. Moving the point in the white grid changes the geometry of the picture. Play with it to see variations of the image.
Additional Reading
[ ℰ ] Bart, Anneke, and Bryan Clair. “Math and the Art of M. C. Escher.” EscherMath, July 8, 2012. https://eschermath.org/wiki.html.
The 20th century Dutch artist Maurits Cornelis Escher was a master printmaker, whose works were heavily infused with ideas from mathematics. This textbook is intended to support a mathematics course at the level of college algebra, with topics taken from the mathematics implied by Escher’s artwork.
This textbook is best when supplemented by one or more printed books about Escher. In particular, Visions of Symmetry contains complementary material on Escher’s life and mathematical approach to symmetry, and Magic of M.C. Escher is an excellent art book that provides a much better view of Escher’s artwork and technique. It is important to remember that artwork viewed on the web is usually small, grainy, and has poor color reproduction.
Throughout the text you will find Explorations, which are short investigative projects to be done in groups in a class setting. Explorations are intended to introduce material in a way that motivates and prepares the student for the more rigorous approach in the body of this text.
“Droste Effect.” Wikipedia, June 29, 2026. https://en.wikipedia.org/wiki/Droste_effect.
Fuyu, Chen, YunFang Liu, Yan Lin, and PeiChang Ouyang. “MATHEMATICS IN M.C. ESCHER’S GALLERY.” World Journal of Educational Studies 2, no. 4 (2024): 55-59. Accessed August 19, 2026. https://doi.org/10.61784/wjes3021.
M.C. Escher, a Dutch graphic artist, is renowned for his masterful integration of mathematical concepts into his art. His work, particularly the piece Gallery exemplifies the seamless blend of art and mathematics, showcasing the beauty and complexity inherent in both fields. This paper delves into the mathematical structures underlying Escher’s Gallery exploring the principles of complex transformations and wallpaper groups. By analyzing these elements, we aim to uncover the profound connections between art and mathematics, and how Escher’s work challenges our perception of reality.
[ ℰ ] Lenstra, Hendrik, and Bart de Smit. “Escher and the Droste Effect.” Universiteit Leiden. Accessed August 19, 2026. https://pub.math.leidenuniv.nl/~smitbde/escherdroste/page_menu=intro&sub=project.html.
This project is an initiative of Hendrik Lenstra of the Universiteit Leiden. and the University of California at Berkeley. Bart de Smit of the Universiteit Leiden runs the project. Their joint paper is the main resource for this site.
Lenstra, H. W. Jr, and B. De Smit. “Artful Mathematics: The Heritage of M. C. Escher.” Notices of the AMS 50, no. 4 (2003): 446-451. Accessed August 19, 2026.
Leys, Jos. “The Mathematics behind the Droste Effect. This Article Uses jsMath Which Requires Java.” Mathematical Imagery, December 26, 2008. https://www.josleys.com/article_show.php?id=82.
Reinder. “Escher and the Droste Effect.” reindernijhoff.net, May 2, 2014. https://reindernijhoff.net/2014/05/escher-droste-effect-webgl-fragment-shader/.
Videos
This project was done a the University of Leiden and the video was taken from their site located at http://escherdroste.math.leidenuniv.nl/
[ ℰ ] This exceptional reference is highly recommended for your consideration.
The featured image on this page is from the StockCake website.