Escher's Droste Effect

Published on 17 November 2008

The "Droste effect" derives from a Dutch chocolate maker that used an image of its box on the box recursively at smaller and smaller scales.

MC Escher's "Prentententoonstelling" (print gallery) image took this idea one step further and mapped the image on itself in a spiral. However, he only got so far with pen and paper leaving an enigmatic white centre. It wasn't until the Dutch mathematician, Hendrik Lenstra, worked out the maths behind the image transformation that the complete effect could be visualised. Take a look at the illustrated write-up that gives a good explanation about the process.

Jos Leys took the process further and created a generic logrithmic image transformation that can create endless zooming animations. This process was turned into a Mathmap script by Josh Sommers and Briec and now has an active Flickr group that use it.

I've ported the Mathmap script over to Adobe's new Pixel Bender Toolkit. Pixel Bender was officially released as part of the CS4 suite but is also available as a free download. The filters will run in After Effects, Photoshop CS4 and Flash 10 (in some cases) so there is huge creative potential here!

See the project page for download and usage instructions

Tags: Patterns, Pixel Bender, Recursive   Last updated: 28 November 2008

13 Comments

• Tomek // Og2t commented at 18 November 2008 at 09:34

  Can't wait to try to PhotoShop filter out, how did you manage to stop Ethan moving the train too far? ;-)

• Frank Reitberger commented at 18 November 2008 at 15:42

  Too bad!

  I really thought I would have enough time to adapt my Droste Effect AS3 Version (I´d developed last week) to Pixel Bender. I wonder where your initial spark came from... ;)

  But anyhow, very nice work!!!

  Cheers
  -frank

• Tom commented at 18 November 2008 at 15:59

  Cheers Frank, if I'd seen your version first I might have saved myself some work. Interesting site BTW, it's now in my list of feeds :)

  Like you I first came across the effect via the Flickr group and my version is a fairly straight port of the Mathmap code described there, with a few extra bits for dealing with the complex number math.

  I'm still working on a Flash compatible version of the filter. However when running in Flash the filters won't use the GPU so I'm not sure if the performance hit will be worth it.

• Frank Reitberger commented at 20 November 2008 at 15:33

  No prob at all Tom,

  to be honest, your port is a solid Pixel Bender version. I shouldn´t have just thought about transforming my AS3-approach for Pixel Bender instead of not porting it right away. So I guess it´s, first come, first served!

  I think it´s definitively worth it, that you work on your Flash compatible version, because even if it won´t use the GPU, it should run quite faster then a native flash analog.
  Anyway, there are so many other nice filters-ideas still remaining, there´s enougjh to play with for everyone... ;)

• mohan commented at 25 November 2008 at 13:53

  Nice thing....but this idea is great......good use of the script

• Frank Beltran commented at 28 November 2008 at 07:47

  Hi guys, I'm Frank Beltran and I made a Droste Videoclip a couple of months ago called "Clap your brains off"...
  Hey this plugin seems great!!! We had to program a code on Java and run a batch on it in order to obtain the images for the video... It was a bit of work, but also a fun process.
  So now there's a plugin... WOW!!!
  Sure things go fast these days...
  I wanted to ask all of you guys that already tried it... (Cause I don't have CS4 or AE so far) How long does it take to process the images???
  Cause part of why we did everything with Java was that with mathmap a 3456 x 2304 pixels image took almost 20 minutes to process... Is it the same more or less with photoshop or it goes way much faster? And how about on AE???
  I'd really appreciate that sort of feedback.

  I'll leave you the link from my video, hope you also see the making of and take a look at the amount of work that was doing it the "hard way"

  Congratulations on your job.

  http://www.vimeo.com/1689442

• Tom commented at 28 November 2008 at 09:10

  Thanks Frank - your amazing video was part of the inspiration for creating the Pixel Bender version!

  Performance wise in After Effects I can tweak the parameters and see the results close to real-time for a D1 PAL video frame (so about 768x576px). However, I don't think that After Effects makes full use of the GPU unlike Photoshop CS4 because with that I can get very responsive updates when changing the parameters on an 8Mpix photo. Either way significantly faster than Mathmap :)

• Dorus commented at 28 November 2008 at 11:51

  I love it! Thanks.
  Immediately tried it in after effects and works beautiful even in animations. And it is much faster then math map (in gimp). Fantastic; keep up the great work.
  (first experiment here: http://dorus.oerlemans.tv/?p=46 (post in Dutch though ))

  Cheers,
  Dorus

• Josh Sommers commented at 1 December 2008 at 20:40

  Hey, this is great! I've been working on a straight Droste Filter for Photoshop for some time, but I gave up a while back because the Photoshop filter architechture was very difficult for me to understand, even as a software developer.

  FYI, the formula you have seen in Mathmap and derived your plugin from was not developed by Jos Leys. The first version was initially developed by my friend Ben (Breic). Subsequent versions, which included all of the little variations you have included in your plugin (like the mirror effect, show both poles, tile poles, pole rotation, etc) were developed by me, in some cases with additional input from Breic.

  My goal has always been to share this effect with the masses, which is why I have always kept the formula public, and is also why I was working to get the effect into Photoshop one way or another. It seems you have achieved that here, and even more importantly, into After Effects. It's really only a matter of time now before we see this effect everywhere, and sadly, those of us who have been at the forefront of the effect and played some part in bringing it to the masses will likely be forgotten. :(

• Andrew Donaldson commented at 10 December 2008 at 11:24

  I was just watching Frank's excellent video again (http://www.vimeo.com/1689442) and noticed that at 1:47 when the guy is flicking through the albums, there are a few famiilar names in there... Nice hat-tip!

  Maybe thats super obvious, but it passed me by the first few watches... :)

• Frank Reitberger commented at 10 December 2008 at 14:04

  Hi again!

  I´ve just rewritten my version of the Droste Effect with Pixel Bender and this one is for the use with Flash too.

  Ok ok... there are still a lot of the origin Math Map values missing - let´s say it´s a lightweight variant. But it´s pretty fast performing when it comes to Flash. :)

  So here it is - enhanced Escher for Flash:
  http://www.dasprinzip.com/prinzipiell/2008/12/10/enhanced-escher/

• Tom commented at 10 December 2008 at 14:10

  35fps - nice :)

• Frank Reitberger commented at 16 December 2008 at 09:48

  ...and as you asked for Tom - here goes the pbk-File:
  http://www.adobe.com/cfusion/exchange/index.cfm?event=extensionDetail&loc=en_us&extid=1706526

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