Droste effect

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The woman holds an object bearing a smaller image of her holding the same object, which in turn bears a smaller image of her holding the same object, and so on.

The Droste effect is a specific kind of recursive picture^[1], one that in heraldry is termed mise en abyme. An image exhibiting the Droste effect depicts a smaller version of itself in a place where a similar picture would realistically be expected to appear. This smaller version then depicts an even smaller version of itself in the same place, and so on. Only in theory could this go on forever; practically, it continues only as long as the resolution of the picture allows, which is relatively short, since each iteration exponentially reduces the picture's size. It is a visual example of a strange loop, a self-referential system of instancing.

[edit] Origin

The effect is named after a particular image that appeared, with variations, on the tins and boxes of Droste cocoa powder, one of the main Dutch brands. It displays a nurse carrying a serving tray with a cup of hot chocolate and a box of the same brand.^[2] The brand's effect, maintained for decades, became a household notion. Reportedly, poet and columnist Nico Scheepmaker introduced wider usage of the term in the late 1970s.^[3]

The Droste effect was first used in 1320 by Giotto di Bondone in his Stefaneschi Triptych. The polyptych altarpiece portrays in its center panel Cardinal Giacomo Gaetani Stefaneschi offering the triptych itself to St. Peter^[4].

[edit] Other examples

A recursive image of a clock face illustrating the Droste effect. The creation of this image was influenced by the work of M.C. Escher. It was rendered using the Mathmap plugin for GIMP and the Droste Effect Formula provided by artist Josh Sommers.

The American mock pundit Stephen Colbert has a portrait of himself on the mantle of his set's fireplace which makes use of the Droste effect. A new one is painted each season, with one more level of recursion added.

In SpongeBob SquarePants, there is a photograph of Mrs. Puff standing next to her doorway, where the picture is located.

Other recursive logos:

• Pink Floyd's Ummagumma album cover
• Land O'Lakes Tub
• The Laughing Cow (La vache qui rit)
• Knights of the Lambda Calculus
• Smarties
• Old bags of Tayto crisps ^[5]
• Mackó sajt (type of cheese in Hungary)
• Paletón Corona (Mexican chocolate covered marshmallow candy)

[edit] See also

• Audio feedback
• Fractal
• M. C. Escher
• Mise en abyme (in French)
• Optical feedback
• Recursion
• Self-similarity

[edit] References

[edit] External links

Wikimedia Commons has media related to: Droste effect

• Escher and the Droste effect
• The Math Behind the Droste Effect (article by Jos Leys summarizing the results of the Leiden study and article)