Monday, 30 March 2009

Last visible Droste

Dr C's "Friday Crab Blogging" series is always fun: children's unusual and creative drawings of crabs. But one of the artists of Friday March 27th will go far: as Dr C says, "You've got to appreciate the detail on this one's tee-shirt", which includes one level of the recursive Droste effect, named after the image-within-image on the label of a Dutch cocoa brand 1. See Droste Effect Packaging at Box Vox for other commercial examples.

Bonzo Dog Food For Thought at Isn’t it infomantic? has another example, the cover of a 1918 book called Khaki Comedy, and mentions Russell Hoban's excellent fable The Mouse and His Child in which the Beckettian play The Last Visible Dog takes its name from the Droste-style label of the book's fictitious Bonzo Dog Food (image and explanation here at The Last Visible Dog blog, and it can also been seen from around 36mins 20secs onwards in the rather creaky animated version).

Ignore the maths on this bit and just enjoy the pictures if you want.

A while back I ran into an interesting site, Escher and the Droste effect, which reports on a study to determine the mathematical structure of MC Escher's Prentententoonstelling (Print Gallery). An American Mathematical Society paper, The Mathematical Structure of Escher’s Print Gallery (B. de Smit and H. W. Lenstra Jr., Notices of the AMS, Vol, 50, #4) goes into the detail. The authors not only derive the function, completing the drawing by filling in the self-similar core that Escher left as a blur, but derive variants including a hypothetical undistorted version. Other artists have used the resultant mathematics to similarly extend Escher's and other works, as well as create original images: see Jos Leys' Droste effect gallery and Josh Sommers' Droste Effect Flickr series, which puts the manipulation to surreal, in some cases nightmarish, use (via the Escher Droste effect formula and Mathmap).

End of mathematical bit.

Scenes-within-scenes (not necessarily recursive Droste-style nor even pictorial) are also called mise en abyme in heraldic and various artistic/literary contexts. Amateur d'art (an arts blog hosted by the French newspaper Le Monde) has a post Un cabinet d’amateur, in relation to the work of Georges Perec, mentioning the use in conversation pieces such as the paintings-of-paintings capriccios I mentioned in Architectural fantasies a while back (it gives as example one of the "kunstkamers" - only three are known - of Willem van Haecht). However, I'd never noticed Group Bel's brand "La vache qui rit" (the Laughing Cow ®) logo to be approximately recursive.2

1. A number of sources, such as Henrik Lenstra in the Paradiso science lectures compilation Het raadsel van informatie (The Riddle of Information, B. Mols, Johan van Benthem) track the coinage of the term "Droste effect" to the writer and journalist Nico Scheepmaker in the 1970s.
2. Nor had I realised its venerability. See for more works by its creator Benjamin Rabier (1864-1939). According to the Bel official site, the original Laughing Cow - which I find a wee bit sinister - was painted on WW1 army vehicles when Rabier was in the same unit as Bel's co-founder Leon Bel.

- Ray


  1. Felix "Growlery" Grant escaped on his nostrilopede -- from the Gödel loop of infinite regression.

  2. I didn't know the term "Droste" until reading this - yet another expansion of my vocabulary for which to thank you!

  3. I mentioned the same topic in 2003 and 2006 in The Apothecary's Drawer, but that was just the raw mathematical graphics; this one is more matured.

  4. Must have either missed or forgotten those two...

    ...just checked them, and they return to me. So I didn't miss them - I subsequently forgot the word.

    Goldfish man strikes again...