Video feedback is a well-known phenomenon which occurs whenever a video camera is pointing at its own monitor. It is quite a popular phenomenon: It is mentioned in numerous books on popular science (for example Gödel, Escher, Bach by Douglas Hofstadter), it is 'practised' by many enthusiasts with scientific and/or artistic inclinations (for a good overview see The Ultimate Video Feedback Page), and it even has a weekly half-hour TV show devoted to it (on a New York cable TV channel).

Video feedback has been researched in considerable detail in the days when cameras and monitors were still based on scan lines. Nowadays, however, both cameras and monitors are pixel-based. We investigated video feedback in the light of this change in technology, and were surprised by our findings.

We became interested in video feedback with pixels as an analogy to a mechanism present in certain laser resonators which leads to fractal structure in laser modes. Just for fun we investigated pixellated video feedback in a bit more detail: We wrote a little simulation program in Java and also did some experiments. The key to getting the experiments to work was to use the 'motion-blur' function of our camera to remove most flicker-related problems. To our great surprise our model generated stationary patterns in the shape of 'classic fractals', like for example Sierpinski gaskets and von-Koch snowflakes - we had encountered another popular topic at the interface between Science and Art (see, for example, A Fractal Art Gallery)!

For our experiments we did not have the right monitors available to create Sierpinski gaskets and von-Koch snowflakes. We did, however, manage to create a few other, really nice, patterns experimentally, like for example a self-similar rosette, Cantor Bars, and the beautiful spiral shown on the right.

How does this fit into other people's work?

We were not the first to create fractal video-feedback patterns. Many people use modified video feedback - using, for example, added mirrors, multiple cameras, multiple monitors, or multiple lenses - to create fractal patterns. Even in unmodified video feedback fractals had been observed, although all of them evolved rapidly in time: There are a few mentions of complex bursts of brightness in the scientific literature (cited in our articles, see below) and on the internet (e.g. Fractal Feedback! and Video Feedback), in some case even recognising the importance of the pixels! Stationary fractal structure had been predicted theoretically by Andersen and Petersen, who simulated video feedback on a matrix model (which corresponds roughly to a screen with square pixels) and found fractal spirals.

So what was our contribution? We described in detail the mechanism that created these patterns, namely iterated pixellation and magnification. This was backed up by extensive computer simulations and our own experiments. In addition, we pointed out what nobody had discovered - or even suspected - before, namely that unmodified video feedback can create 'classic fractals', like the Sierpinski gasket mentioned above. By knowing exactly what we were looking for, and by accidentally discovering that our camera's motion-blur function removed most flicker-related problems, we were also able to create the first stationary fractal patterns using unmodified video feedback.

KEY PUBLICATIONS

Johannes Courtial, Jonathan Leach, Miles J. Padgett, Image processing - Fractals in pixellated video feedback, Nature 414, 864 (2001) Jonathan Leach, Miles J. Padgett, and Johannes Courtial, Fractals in pixellated video feedback, Contemp. Phys. 44, 137-143 (2003) J. Courtial and M. J. Padgett, Monitor-outside-a-monitor effect and self-similar fractal structure in the eigenmodes of unstable optical resonators, Phys. Rev. Lett. 85, 5320-5323 (2000)

SEE ALSO

some online reviews of this work:

• Pixel feedback forms fractals
  TRN News
• Optische Rückkopplung - Kamera plus Monitor erzeugt Fraktale (in German)
  Bild der Wissenschaft online Newsticker
• Die etwas anderen Fraktale (in German)
  GIGA

journal & newspaper articles:

• Fractals on video, PhysicsWorld, February 2002, p.25
  JPEG (73K)
• Physiker lassen Schneestürme über den Monitor toben, Die Welt, 24 December 2001, p. 31 (in German)
  JPEG (61K), access through Die Welt's web page
• Er is een labiele laser op tv, de Volkskrant, 22 December 2001, wetenschapsbijlage, p. 3 (in Dutch)
  JPEG (342K)

CONTACT

Detail from a video-feedback fractal based on the Cantor set. After being recorded experimentally it was coloured in with dubious taste, creating a tartan-like appearance.

Fractal video-feedback spiral. This stationary pattern was created experimentally with a rotated camera; it was coloured in afterwards.

Simulated formation of a stationary fractal video-feedback spiral.

How pixels lead to fractal video-feedback patterns. The centre and right columns show the respective images recorded by the camera and displayed the screen. On the screen, the field of view of the camera, i.e. the area the camera will record during the following feedback iteration, is marked with a red rectangle. n is the number of feedback iterations, starting with the camera seeing a uniform white (n=0).

Some simulated video-feedback fractals (clockwise from top left): Sierpinski Gaskets, Cantor Bars, tartan, von-Koch Snowflakes (black areas).

Simulated formation of a stationary Sierpinski-gasket pattern.