Here's a way to generate fractals with video hardware in real time. First, create a video feedback loop. Do this by aiming the video camera at the monitor. The monitor and camera settings are important, try the following general setup: monitor brightness all the way down, or at least very low (not completely black, obviously). Contrast set somewhat higher than normal. Zoom the camera in so that the *image* of the monitor on the monitor is about the same size as the monitor (in other words, aspect ratio close to 1:1). Also, some rotation is desirable, else you just get a blob that is hard to stabilize. Hint: turn the monitor upside down, or put it on its side - this is much easier than trying to mount a camera upside down on a tripod! Oh yeah, tripods are good. Adjust the tripod so you can rotate the camera about the viewing axis. At this point you should be able to create lots of swirling, spinning stuff. Try messing with the color, (B&W is usually easier to start with), phase, focus, zoom, iris, etc. If the camera and or monitor has automatic features, turn them all off, you get better control that way. Try poking your fingers in, or shining a flashlight on the screen. The patterns that you see can exhibit spatiotemporal oscillation and chaos, and can be quite hypnotic. But there is usually a single fixed point on screen (that is either stable or unstable, depending on the zoom). To get more complicated patterns like fractals, you need to mix in another transform. The simplest way to do this is with a mirror. The setup should look like this: monitor | video camera | ___ +-->| >___|---+ | | ----------------- | | | mirror | | | +------------------------------------+ The mirror is positioned so that the camera sees *both* the monitor screen directly, and a reflected view of it. Now you have two transforms of the image to play with: the non-linear transform provided by the electronics of the camera+monitor, and the simple reflection of the mirror. With the setup above I have been able to create colorful, pulsating, fractal ferns, and some 'jellyfish' like shapes. Quite different from the usual video feedback fare, because of the break from circular symmetry. Almost like life-forms. Another way to do this is with a video mixer. Point two cameras at the screen, mix their output together and display it on the screen. With different rotation angles and zoom settings it is possible to create lots of cool visual effects. You can also try this with the poor man's video mixer, a half-silvered mirror. I've been able to get some interesting patterns, but there are some serious constraints on this method. Video feedback is cool in general, and I encourage anybody with a camcorder to point it at the monitor screen! (Remember to rotate it, and zoom in to close to 1:1.) It is a great way to demonstrate nonlinear, self-organizing pattern formation. I have had people look at the screen and say "where does the pattern come from?" This is a great excuse to start telling them all about dissipative structures, reaction-diffusion systems, etc. etc.. Once I even got a pattern of spiral waves that looks a little like the BZ reaction. There are several sources for more information about video feedback. One is this paper, which discusses the mathematics (there is a video tape to go along with this paper, I don't know if it's still available): J.P. Crutchfield, "Space-time dynamics in video feedback," Physica 10D (1984) 229-245. Another is the book by H.-O. Peitgen, H. Juergens, and D. Saupe, "Fractals for the Classroom" (vol. 1) 1992, Springer-Verlag, New York. This book has some pictures of video feedback, as well as quite a lot of information about pattern formation through iterated mappings. It was Dr. Peitgen's suggestion to use a mirror, by the way. Some more mathematics and inspired musings can be found in the excellent book by A.V. Gaponov-Grekhov and M.I. Rabinovich, "Nonlinearities in action: oscillations, chaos, order, fractals" 1992, Springer-Verlag, Berlin. For information about the Fractal Report, send email to: John@longevb.demon.co.uk