How to produce fractals without a computer

[Video Link]

Via the BB Submitterator, TheOtherMichael points us to a nifty YouTube video of...

Computer-free fractals using "light on a wall as memory and the physical geometry of the path taken by the light into the camera and out from the projector as the processor to calculate the appropriate affine transformations." A lot of familiar fractal patterns show up -- and the universe itself is the computer.

Blew my mind. I hope Mandelbrot got to see something like this before he died.

From the video description, by YouTube user YummyFuture:

Video feedback is a well-known phenomenon. If you hook a camera up to a TV and then point it at the TV, you get an infinite regression of images. However, you can use the same feedback phenomenon with multiple displays to make fractals. By displaying multiple smaller copies of what the camera sees, photographing that cluster of copies, and then repeating the process, you essentially create the self-similar structure seen in fractals. By moving and rotating the camera and projectors, you can create a very wide variety of fractal images.

The images seen in this video are not software-processed in any way. The camera is plugged in directly to the projectors. The pulsing and color shifting comes from the white balance and gain control of the camera.

In this setup, we're "computing" the fractal by using light on a wall as memory and the physical geometry of the path taken by the light into the camera and out from the projector as the processor to calculate the appropriate affine transformations. Given that both TV cameras and video projectors were around back in the late 1940s, it's possible that someone could have done this sort of setup at the dawn of the computer age.

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  1. No need to put “computing” in quotes – an analogue computer is still a computer and at one point it was an open question as to whether we’d go down the analogue or the digital path for computing technology.

    The original opening credits for “Dr. Who” were based on video feedback.

    I don’t remember the details but sometime around the early 90s there was an experiment involving chaotic phenomenon, something to do with magnetic particles suspended in a super-cooled super-conducting fluid, where the end result was a Mandelbrot snowman.

    1. This isn’t really analog computing, though, where the circuits actually make computations using analog signals. The only thing they’re doing here is amplifying, and then using optics to scale and rotate. Which might be “computing” in a very weak sense, but definitely isn’t what they were doing with op-amps back in the day.

  2. trippy. I think the makers of Dr Who used this technique back in the 60s to create the title sequence.

  3. Amazing. Analog “computing” is happening as fast as the camera can process it. Seems much faster than a digital computer trying to calculate multiple fractals.

  4. I don’t have it handy, but GEB had some images of a TV camera pointed at its own output, and I seem to recall some of them looking rather fractalish. He didn’t take it this far, though.

    1. It’s generating a specific kind of fractals called Iterated Function Systems. Waclaw Sierpinski is among of the discoverers (“Sierpinski Triangle”, google it)

    2. It’s more than a kaleidoscope, because of the self-similar repeating patterns. If you look at any edge of one of those fractals, you’ll see the same fractal repeated to infinity — or at least, to as far as the resolution of the camera and projector allows.

  5. The universe is the computer, yes — analog (we presume) and so the computations are blinding fast, but the algorithms lack some flexibility. The precision of the data is relatively high, but limited fundamentally by the design of the device.

    Now, could this somehow be done with mirrors and lenses? that would avoid the precision-limitation of the video-camera’s resolution, but we would have a light lossage as it passes back and forth from mirrors and through lenses (and air) — is there anyway to amplify it non-electrically, without introducing too much noise?

  6. Too complicated! All you need is normal video feedback with one monitor, but with a mirror in the path.

  7. For the ‘Edge of Chaos’ exhibit at Museum of Science we made this effect interactive: color video feedback, a perpendicular mirror down the center of the video monitor, and a slot for placing your hand in the path. Buttons to zoom the camera in and out. Rather than the “infinite tunnel” of normal feedback, the mirror divides the tunnel in 2,4,8 …fractal dimension. Tilt the camera so the tunnels aren’t all on a horizontal line.

    The result was a fractal tree/kidney/broccoli shape. If you hand was in there, you’d have an infinite number of fingers. Mess with color balance and you can produce dynamic color mapping just like Mandelbrot animated GIFs.

    One thing I never got around to trying: fractal ferns. First set up video feedback, then tilt the camera to produce a spiral. In theory you should be able to place a mirror segment in the scene, where the mirror reflects the infinity point, and the mirror is placed near the start of the spiral. The spiral should then be composed of branches where each branch is a copy of the entire spiral.

    A similar trick, if combined with a deformed mylar mirror, should produce Julia sets, no?

  8. Okay, this uses a computer (three, actually), but I find it fun…

    With Macintosh screen sharing (or whatever is the equivalent on Windows) use screen share on computer A to display the screens of computers B & C. Size and arrange them to your liking.

    Now on Computer B use screen sharing to display the screens for A & C. (You can do this easily since you already have access to computer B via the shared screen.)

    Similarly on computer C, use screen sharing to display A & B.

    Grab some windows and move them around. It helps if each computer has a different overall color of screen background.

  9. The Curiosity Collective had fun experimenting with geometric transforms like this to create fractals a couple of years ago.

    http://cefn.com/blog/kaleidoscope.html has video and a screensaver which uses your built in iSight camera on a Mac to give you a similar effect.

    This saves you needing 3 projectors in order to get the fractal effect (thought 3 projectors is analoguer and cooler in many ways).

    Just point your iSight camera at a screen, or get a mirror if the iSight is in the screen.

    http://curiositycollective.org/v2/projects/ for more Curiosity.

  10. Well, thanks a LOT. My mind is now officially BLOWN. Good luck to me to I ever pick up the pieces again.

    Seriously though, that was like out of some science fiction movie where, dude iterates a deep section of Pi and comes out with a message from extraterrestrials. Just from video feedback you get an instantly recognizable Mandelbrot set?? WHO KNEW? (Uh, and sorry about the caps and punctuation– I mean my mind IS blown, and all…)

  11. The music, by the way, is an absolute choice cut of early ambient dub…

    Papua New Guinea by The Future Sound of London

  12. I played around with fractal video feedback in the 90’s. A few years ago someone wrote an article about fractal video feedback for the journal “Fractals” and used it on the cover. One of the things not mentioned above is to crank up the saturation and tint on your video camera and you get really nice rainbow color changes each iteration through the camera. It really is hours of fun. Just get a cam point it back at your screen and stick a mirror in the side, till you get double recursions in both the mirror and the screen.

  13. @Sic Transit Gloria: YES! And, for the uninitiated, GEB refers to the epic Gödel Escher Bach: An Eternal Golden Braid by Douglas Hofstadter. A must-read for people interested in logic, computing, patterns, fractals, and emergent behaviors…

    @Bill Beaty: The Edge of Chaos exhibit? At which MoS, Boston’s? I wish I had seen that! Sounds amazing!!!

    Some friends and I started a video performance art group in Boston, MA, USA in the mid-1990’s called Noise Laboratories, and we spent a lot of time exploring and producing video feedback. (In fact, our 1996 vintage web site persists to this day at http://www.noiselabs.com!) We were astounded to find these patterns of nature arising spontaneously in what seemed to be a relatively simple physical/optical/electronic system. We would create shows where the spectators would become participants, creating and interacting with the video feedback. We used the video feedback signals as inputs to video mixers and special effects generators that allowed us to layer three or four video streams in real time.

    We found that the old analog TV sets (in particular, the 1980’s RCA ColorTrak models) provided the best results, as these sets had manual controls (usually knobs) for adjusting color saturation, hue, brightness, and contrast. If you checked one of these on a waveform monitor or vectorscope, you’d likely see that the color saturation was probably well outside of “legal” NTSC limits, which made it all the more fun! These days, it’s hard to find a display system that isn’t digitally quantized…

    Also, in terms of Analog Computing, you might be interested in the Sandin Image Processor, a patch-programmable analog Video Synthesizer invented by Dan Sandin in the early 1970’s (see the Wikipedia entry for details). I was lucky enough to work with one of the original Sandin IP’s at the Experimental Television Center in Owego, New York… such a thrill!

    Shouts-out to the NoiseLabs crew — Toshi, Matt, Mark, Brett, Chicken, Dave, Ben, John, Joey, Merin & all the rest!

  14. What I want to know is: would there be a way to do something like this with ONLY mirrors? Because 1) it would be helpful for the next time I get stranded with my time machine (obviously) and 2) because you would be computing (not in quotation marks :-P) at the speed of light (taking advantage of the processing power of the universe) instead of having to wait for the 60 fps or whatever lag of the video camera (or your clunky pc) to do the recursions…

    1. fractals with ONLY mirrors:

      Take three spherical mirrors (silver Christmas tree ornaments or large polished ball bearings work well).

      Make a triad of them each touching the other two.

      Look at the reflections made in the central triangular opening…

  15. Here are some very strong examples of video feedback that I made. These go light years beyond the obvious Iterated Function System “look”. I used realtime video synthesizers, such as the Sandin IP, on several of these videos.

    http://www.dr-yo.com/video_machina_comp.html

    “Coils of the Worm” is the purest example I have of a complex video feedback setup. This used four cameras and four monitors, all feeding through three Grass Valley Group analog switchers and a Hearne/EAB Videolab II.

  16. For those who are interested, the music credits are:

    Future Sound of London – Papua New Guinea
    Cygnus X – The Orange Theme (Solar Stone Remix)

    :)

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