Simulation of video feedback

Michael Cramer Andersen and Jesper Petersen. August 1996.

Introduction

What is video feedback? And what does it say about life and complexity?
The Video Feedback (VF) experiment is simple in nature, but complex in behaviour . It has been known to TV producers for decades and has an analogue to audio-feedback, which is just 'amplified noise'. VF is closer to Art than to Science even though the ingredients - tele-vision and video-camera are high technological products of science and industry. You can perform the experiment in your living room, and even the cheapest equipment will work well.

Real video feedback

VF is a complex dynamical system which makes beautiful spatial patterns which evolve in time. The patterns are made of light which is trapped in a loop: The camera points towards a screen which is showing what the camera has just 'seen'. First you will see a picture in a picture in a pict.... But when tilting the camera, zooming in, and initiating the pattern with some lightsource in a dark room, the experiment is on! Even though it has no direct applications, it is a relatively simple system, still available to study evolution in a self organized system at the Edge of Chaos; Another advantage is that it evolves with 25 generations a second, and no animals are hurt! :-) The steps towards a succesful VF-experiment are as follows:

Connect video camera and monitor, so 'live' recording is possible.
Turn the camera against the monitor approx. one meter from the screen.
Zoom in/out (or move camera back and forth) until you see "a picture in a picture"...
Tilt the camera around its optical axis (from the center of the lens ortho gonal to the monitor screen). Zoom in and watch the effect at different angles.
Turn off the light in the room and place a light source (e.g. a candle or a lighter) between monitor and camera.
Now you should be experimenting pretty well, and you can start varying the parameters on the monitor/TV-set: brightness, contrast and the cameras: zoom , focus and orientation.

At a certain point, the feedback system 'takes over' - you just don't wait to manipulate the controls, waving your hands between the screen and the camera or light on the picture. You just want to see: "What happens next?". It can go into a chaotic attractor, when new patterns are following each other. See the large panel with a great variety of patterns. They are all snapshots from hours of video feedback experiments.

Simulation of video feedback

We will now turn to the mathematical model which was worked out by J. P. Crutchfield in 1984. It describes an image as a 2D structure - a matrix - which can be rotated, magnified and so on. The details are not so important here: but the new picture consists of 3 components:

The old image stored in the camera
Spatial coupling to neighboring pixels (controlled by focus)
The incoming image from the monitor screen. This is possibly rotated and magnified.

Click on the formula to read it...

This model is perfectly fitted for computer simulation. Since 1984 computers has improved, and it is now within the limits of computation time to investigate the parameter space, possible in VF. The two most important parameters are: rotation angle v, and zoom factor z which is slightly below or larger than 1. The two cases will be treated separately in the next section.

Results

There are basically two kinds of behavior in video feedback: When the zoom is less than unity, the points of light are dragged towards the center along spiral paths, acording to the rotation angle and zoom. When zoom is larger than unity, the tiny details at the center, including noise, are magnified to fill out the whole image and beyond.

Because of the finite resolution of the screen, pixel truncation is also an important factor in the creation of structure.

The first case (z<1) can easily be investigated with the computer model and compared with experiments. With a laser diode point light source, the following images were made:

Fig.: Real video feedback: A point light in the top of the picture forms spiral patterns according to the rotation angle. Approximate angles: 0^o 23^o and 70^o. Second row: 72^o, 90^o and 115^o. Third row: 120^o, 165^o and 180^o.

Fig.: Simulation of a constant point source feeding light inwards to the center along (discrete) spiral paths depending on the rotation angle. The angles chosen are all divisors of 360^o. Other parameters: B=0.90; L=0,20; z=0,96. Total number of iterations: n=100.

In the case of positive zoom (larger than unity), the patterns a re much different. The fundamental form is still the spiral, but now the light is coming from the center and along different kinds of spiral arms towards the border of the screen.

The creation of patterns are different, when the zoom factor is larger than unity. The ten series start with the same initial picture (a vertical line 11 pixels high), but according to the values of zoom and rotation angle, the results changes radically. Because of the combination of rotation and enlarg ement, the patterns develop fractal spirals of all kinds. It is basically noise which is amplified.
The ten series (row 1..10) has the parameters P(v,z) equal to: (13;1.09), (34;1.12), (31;1.24), (34;1.31), (37;1.24), (30;1.50), (43;1.46), (44 ;1.43), (27;1.78), (01;1.97). The iterations go from 1 to 50 where the patterns are fixed. The spiral arms are naturally stabilized in fractal patterns. It could be interesting to map the fractal dimension of the found spiral pattern s in the whole parameter space. You could of course also change the initial imag e, and see what influence it has on the creation of patterns.

Escape

This is only a small appetizer of what kind of behaviour that is possible in video feedback. There are still many questions that are not answered, and not even proposed.

References

J. P. Crutchfield: Space-time dynamics in video feedback, Physica 10 D (1984).
M.C. Andersen: Mønsterdannelse i simuleret videofeedback (abstrakt). Bachelorprojekt, Københavns Universitet 1995.