Droste or Recursive Images

[David]

In a recent post, I drew the attention of GIMP users to an extensive plug-in called MathMap. Amongst other features there is an option to create Droste or recursive images. A recursive image is one that has the image repeated within itself, ad infinitum. The effect can be easily illustrated by placing two mirrors parallel to one another. Any object placed in-between the mirrors is then reflected, in principle, an infinite number of times. The term "Droste" comes from an advert from the early 1900's (for chocolate?) featuring a recursive image.

The MathMap Droste option has 28 (sic) control sliders and appears to have been written for Linux versions of the GIMP. In addition, the tutorials are confusing and the the application is, in my hands, highly frustrating. Consequently, I decided to capture some real Droste images. For this I've used my Canon 40D fitted with a 24-105mm EF zoom lens. I connected the camera to my computer and activated the EOS Utility software, selecting the Remote Live View option. If the camera is now pointed at the computer screen, a recursive image of screen appears. If anyone wishes to try this, use manual focus on the camera body rather than the focus option in EOS Utility. The first image below shows the result.



The image itself is of the EOS Utility screen and note the histograms on the RHS. There are some interesting features. First, there are about 15 repetitions of the image, gradually reducing in size. Second, most of the colour has been lost, a point to which I will return. Third, there is a texture on the screen. This may be the underlying texture of the TFT screen itself, but I do not know for sure. Fourth, although not seen in the still image, the screen takes several seconds to stabilise. The second image below was captured a second or so after the Remote Live View option was activated. Note how all the histograms are different.



If the camera is rotated, then the angle of rotation is replicated in each of the recursive images. For a large angle of rotation the final image quickly spirals into infinity as seen in the third image.



If the lens zooms into the image strange effects appear as the camera/image tries to establish an equilibrium position.



Note also the blue colour in this image. Such colour appears to pulse through the image taking about 6 seconds to go from the front to the back of the recursion. I really do not understand exactly what is going on with this.

The last image in this post shows an even weirder effect.



What you are seeing is the image of the previous screen that had been on the monitor (EOS DPP with thumb nails and folder display). Simply closing that screen and capturing the immediate recursive image shows the former screen. It eventually, over several seconds, recedes to the background losing size and shape as it does so.

More images can be seen at my PBase site: http://www.pbase.com/david_ws/droste

Comments and explanations are more than welcome.

Cheers

David

[rogerb]

This is most interesting, David.

I can't say I fully comprehend what's going on with the color thing. My feeble engineering mind makes me suspect that the color showing up on the screen is not quite the same as what the camera thought it saw so the recursive action is causing the color to gradually drift in one direction or the other, depending on the direction of color shift from the camera to the monitor. However that really doesn't explain everything. I will need to study this further before being any more assertive.

This'll be a fun and very educational experiment to conduct on a rainy day!
Thanks for posting it.
Roger

[rogerb]

David:

This could be a very interesting way of checking the calibration of the monitor vs. the camera. With everything balanced, nothing should change?

In photos 1 & 2, there is a gradual darkening of the image which would imply that the tonal "gain" in the loop is less than unity (i.e., the monitor displays an image that is very slightly darker than that of the image data output from the camera....or the camera output an image that was darker than what it saw), making each image progressively darker.

The same could be said for the saturation, thereby explaining the gradual loss of color in the images.

However the zoomed shots have me baffled (which happens more and more these days). Can you provide a bit more information on exactly how you zoomed to get those images (specifically #4, was this a fixed tilt but dynamic zoom?)? What is the resolution of your monitor, vs. that of the camera?

Roger

[David]

Hi Roger - Thanks for your interest in this arcane topic. Thanks also for the email. First, I've posted some more "patterns" on the PBase site. If I could control what was going on then I could claim some degree of abstract artistic expression, but so far I can't.

Dealing with your questions: the monitor resolution is 1600x1200, the maximum available for the ViewSonic VP2030b that I'm using. The image sizes are 3888 x 2592 in RAW, but I'm not sure that is what would be displayed in LiveView, as presumably that would be an interpreted JPG image. Nevertheless, your idea (in your email) of interference patterns makes sense. The Zoom-Rotation (and Pattern) images are produced by having the camera at a slight rotational angle (10-15 degrees) to the horizontal and setting the zoom such that the image cannot stabilise, i.e. it keeps hunting for an equilibrium. The zoom is not changing as I take the shot.

I agree with your point about tonal variation in that any difference between camera and monitor will eventually lead to darkening and loss of image quality. This happens in the mirror analogue where you cannot get an infinity of images, noise and discontinuities eventually destroy the images. However, the image will degrade with each iteration anyway because of lack of pixels.

I had not thought about the calibration idea, that would be worth exploring further. It would require test images with appropriate B/W and colour standards. Or maybe not ... I don't know.

Re rainy day - it's raining now - the normal state of the weather here at this time of year. I guess in Texas it's nice and sunny?

Cheers

David