# Droste effect

The Droste effect (Dutch pronunciation: [ˈdrɔstə]), known in art as an example of mise en abyme, is the effect of a picture recursively appearing within itself, in a place where a similar picture would realistically be expected to appear. This produces a loop which mathematically could go on forever, but in practice only continues as far as the image's resolution allows.

The original 1904 Droste cocoa tin, designed by Jan Musset (1861–1931)[a]

The effect is named after a Dutch brand of cocoa, with an image designed by Jan Musset in 1904. It has since been used in the packaging of a variety of products. The effect was anticipated in medieval works of art such as Giotto's Stefaneschi Triptych of 1320. It is seen in the Dutch artist M. C. Escher's 1956 lithograph Print Gallery, which portrays a gallery that depicts itself. The model village at Bourton-on-the-Water contains a model of itself, with two further iterations.

## Effect

### Origins

The mise en abyme effect is named after the image on the tins and boxes of Droste cocoa powder which displayed a nurse carrying a serving tray with a cup of hot chocolate and a box with the same image, designed by Jan Misset.[2] This familiar image was introduced in 1904 and maintained for decades with slight variations from 1912 by artists including Adolphe Mouron. The poet and columnist Nico Scheepmaker introduced wider usage of the term in the late 1970s.[3]

### Mathematics

The appearance is recursive: the smaller version contains an even smaller version of the picture, and so on.[4] Only in theory could this go on forever, as fractals do; practically, it continues only as long as the resolution of the picture allows, which is relatively short, since each iteration geometrically reduces the picture's size.[5][6]

### Medieval art

The Droste effect was anticipated by Giotto early in the 14th century, in his Stefaneschi Triptych. The altarpiece portrays in its centre panel Cardinal Giacomo Gaetani Stefaneschi offering the triptych itself to St. Peter.[7] There are also several examples from medieval times of books featuring images containing the book itself or window panels in churches depicting miniature copies of the window panel itself.[8]

### M. C. Escher

The Dutch artist M. C. Escher made use of the Droste effect in his 1956 lithograph Print Gallery, which portrays a gallery containing a print which depicts the gallery, each time both reduced and rotated, but with a void at the centre of the image. The work has attracted the attention of mathematicians including Hendrik Lenstra. They devised a method of filling in the artwork's central void in an additional application of the Droste effect by successively rotating and shrinking an image of the artwork.[4][9][10]

In the 20th century, the Droste effect was used to market a variety of products. The packaging of Land O'Lakes butter featured a Native American woman holding a package of butter with a picture of herself.[4] Morton Salt similarly made use of the effect.[11] The cover of the 1969 vinyl album Ummagumma by Pink Floyd shows the band members sitting in various places, with a picture on the wall showing the same scene, but the order of the band members rotated.[12] The logo of The Laughing Cow cheese spread brand pictures a cow with earrings. On closer inspection, these are seen to be images of the circular cheese spread package, each bearing the image of the laughing cow.[4] The Droste effect is a theme in Russell Hoban's children's novel, The Mouse and His Child, appearing in the form of a label on a can of "Bonzo Dog Food" which depicts itself.[13][14]

### Model village

A three-dimensional example of the Droste Effect can be seen in Bourton-on-the-Water, England. A model of the village was built within the village in the 1930s at a 1:9 scale, using traditional building materials. It contains within it a model of itself, which in turn includes a further smaller model, and then an even smaller model within that.[15][16]

### Comic books

The Droste effect has been a motif for the cover of comic books for many years, known as an "infinity cover". Such covers were especially popular during the 1940s. Examples include Batman #8 (December 1941-January 1942), Action Comics #500 (October 1979), and Bongo Comics Free For All! (2007 ed.). Little Giant Comics #1 (July 1938) is said to be the first-published example of an infinity cover.[17]

## Notes

1. ^ Johannes (Jan) Musset was born in Haarlem on 8 March 1861 to Willem Jacobus Musset and Catharina Schmidt, and worked as a painter of advertisements. He designed the nurse image for Jan Gerard Droste, based on the painting La serveuse chocolat (c. 1745) by Jean-Étienne Liotard.[1] The Droste tin design was reworked only eight years later by "Cassandre" (Adolphe Mouron) into its more famous form. Musset died in Haarlem on 26 August 1931, so his design is out of copyright.

## References

1. ^ "1863–1918 from confectioner to chocolate producer". Droste. Archived from the original on 4 March 2016. Retrieved 28 February 2018. Around the year 1900 the illustration of the "nurse" appeared on Droste's cocoa tins. This is most probably invented by the commercial artist Jan (Johannes) Musset, who had been inspired by a pastel of the Swiss painter Jean Etienne Liotard "La serveuse de chocolat", also known as "La belle chocolatière".
2. ^ Törnqvist, Egil. Ibsen: A Doll's House, pp.105, Cambridge University Press (1995) ISBN 978-0-521-47866-3
3. ^ "Droste, altijd welkom". cultuurarchief.nl. Archived from the original on 30 March 2008. Retrieved 18 November 2007.
4. ^ a b c d Merow, Katharine (2013). "Escher and the Droste Effect". Mathematical Association of America. Archived from the original on 2 August 2013.
5. ^ Nänny, Max; Fischer, Olga (2001). The Motivated Sign: Iconicity in Language and Literature. John Benjamins. p. 37. ISBN 978-90-272-2574-0.
6. ^ Juola, Patrick; Ramsay, Stephen (2017). Six Septembers: Mathematics for the Humanist. Zea Books. p. 116. ISBN 978-1-60962-111-7. By putting a picture inside a picture, you get a progression of suggessively smaller, but self-similar images (the box of Droste cocoa has a picture of a woman holding a box of Droste cocoa... ). In theory, this nesting could go on forever into infinite detail, but in practical terms, the resolution of the image limits how it's actually drawn.
7. ^ "Giotto di Bondone and assistants: Stefaneschi triptych". The Vatican. Archived from the original on 30 November 2016. Retrieved 23 June 2008.
8. ^ See the collection of articles Whatling, Stuart (16 February 2009). "Medieval 'mise-en-abyme': the object depicted within itself" (PDF). Courtauld Institute. Archived from the original on 2 November 2013.`{{cite web}}`: CS1 maint: unfit URL (link) for examples and opinions on how this effect was used symbolically.
9. ^ de Smit, B.; Lenstra, H. W. (2003). "The Mathematical Structure of Escher's Print Gallery" (PDF). Notices of the American Mathematical Society. 50 (4): 446–451. Archived (PDF) from the original on 16 April 2021. Retrieved 28 April 2021.
10. ^ Lenstra, Hendrik; De Smit, Bart. "Applying mathematics to Escher's Print Gallery". Leiden University. Archived from the original on 14 January 2018. Retrieved 10 November 2015.
11. ^ Barr, Jason; Mustachio, Camille D. G. (15 May 2014). The Language of Doctor Who: From Shakespeare to Alien Tongues. Rowman & Littlefield. p. 41. ISBN 978-1-4422-3481-9. Archived from the original on 10 February 2019. Retrieved 17 October 2016.
12. ^ Den Hartog, Ben (11 November 2011). "The Droste effect on Pink Floyd album Ummagumma". OtherFocus. Archived from the original on 24 November 2015. Retrieved 21 September 2015.
13. ^ Kelly, Stuart (31 December 2013). "The Mouse and His Child by Russell Hoban: moving metaphysics for kids". The Guardian. Archived from the original on 14 November 2017. Retrieved 13 November 2017.
14. ^ "Bonzo Canned Dog Food". Box Vox. 20 November 2013. Archived from the original on 14 November 2017. Retrieved 13 November 2017.
15. ^ Marshall, Brian Robert (8 May 2013). "Model Village, Model Village, Model Village, The Old New Inn, Bourton-on-The-Water". Geograph. Archived from the original on 11 December 2020. Retrieved 17 April 2020.
16. ^ Davies, Caroline (19 April 2013). "Bourton-on-the-Water model village gets Grade II listed status". The Guardian. Archived from the original on 8 December 2020. Retrieved 17 April 2020.
17. ^ Cronin, Brian (15 December 2018). "What Was the First Comic Book 'Infinity Cover'?". Comic Book Resources. Retrieved 19 January 2022.