# Fractals without a Computer!

This is really remarkably clever:

Since I can't stand to just post a video without any explanation:

A fractal is a figure with a self-similar pattern. What that means is that there is some way of looking at it where a piece of it looks almost the same as the whole thing. In this video, what they've done is set up three screens, in a triangular pattern, and set them to display the input from a camera. When you point the camera at the screens, what you get is whatever the camera is seeing repeated three times in a triangular pattern - and since what's on the screens is what's being seen by the camera; and what's seen by the camera is, after a bit of delay, what's on the screens, you're getting a self-similar system. If you watch, they're able to manipulate it to get Julia fractals, Sierpinski triangles, and several other really famous fractals.

It's very cool - partly because it looks neat, but also partly because it shows you something important about fractals. We tend to think of fractals in computational terms, because in general we generate fractal images using digital computers. But you don't need to. Fractals are actually fascinatingly ubiquitous, and you can produce them in lots of different ways - not just digitally.

• Manuel Moe G says:

I briefly saw something that looked like a Julia fractal [ something like http://www.codeproject.com/KB/cs/FractalMaster/frac3.png from The beauty of fractals ; A simple fractal rendering program done in C#; Zimmermann Stephan; 27 Jul 2009 ], but can it really be a Julia fractal? I don't think so.

I am trying to understand this, and the simplest way will be to try to explain it myself, so my ignorance can solicit jeers and corrections.

Each projector + camera is a single complex equation, for a perspective transform. Take a few together, you have a strange attractor, and you have the basis for this video art. But Julia sets don't quite work like that:

http://mathworld.wolfram.com/JuliaSet.html

Since this camera + projector setup cannot create the full range of Julia sets, I don't think it can even generate any (except for the degenerate ones, like a point or a line)

• My favorite fractal-ish thing is a head of broccoli romanesco. I have been known to stand in the kitchen for several minutes staring at one in my hand before I can bear to cut it up for cooking.

• horosphere says:

This reminds me of the Chaos Game method.

I imagine that, technically, all the images they get are the interior of some Julia set, in the sense of being points that are stable under iteration, but I'm not sure how this could produce the "standard" Julia sets. What manipulation of the camera and projectors would be equivalent to squaring a complex number?

I don't know much about weird tricks you can do with cameras so I'm not sure. If anyone else is good with cameras but not math, you'd need something like: 1) a stretching rotation to the left that doubles the visual field, such that the right-center stays the same, the top-center is given a quarter-turn, the left-center is given a half-turn (i.e., will overlap the right-center), and the bottom-center is given a three-quarters-turn (ending up on the left, overlapping what used to be the top-center) 2) a scaling stretch based on distance from a ring around the center of rotation, such that the area inside the ring is squished toward the center, the area outside is stretched outward, and the ring itself stays constant.

On the other hand, I suppose any L-system or simple IFS would potentially work. I think I saw Heighway's dragon in there, which does look kind of like Julia fractals near the cusp of the M-set's cardioid...

• Pirvonen says:

Thank you.
Many bloggers at times post embedded videos with not a single word of explanation. The video might be interesting to watch -- at a later time. But when I am given no information about the contents, I just get annoyed and skip the posting.
Exemplary work. Not only in this regard, but overall in your blog.
//Pirvonen

• andre3 says:

So are they generating different fractals by changing the angle and positions of the projectors or the camera or what? I'm not quite sure what's making the changes to the images, but it looks like they were doing both.

• MarkCC says:

I'm not entirely sure. Based on what they said and watching it, I think that they're doing both.

The video has multiple segments. It looks like in different segments, they're starting with different arrangements
of the three projectors. There's also obviously a lot of camera rotation going on. And a lot of it appears to be just pure chaotic change: the camera is looking at its own output, so you get a lot of chaotic effects.

Frankly, it makes me wish that I had a bunch of displays I could set up in this way with a camera, so that I could experiment myself, and see what it takes to get images like that. Unfortunately, I don't

• There is some discussion of this sort of thing in Hofstadter's "I Am A Strange Loop," the context being the interesting "self loop" effects of this sort of feedback. There are some illustrations, but thanks for the video that shows the effects much more clearly.

(If you liked "Godel, Escher, Bach," I recommend IAASL. It's a good book, sort of a second attempt, if you will, since as Hofstadter puts it, "the fundamental message of GEB ... seemed to go largely unnoticed." There is also IMHO a rather powerful chapter relating some of his ideas to the very abrupt loss of his wife.)

• Jim Cownie says:

The famous Bohemian Rhapsody video http://www.youtube.com/watch?v=fJ9rUzIMcZQ&ob=av2n has some of these video feedback effects.
It was all done before digital video manipulation by using feedback...

• KarenParker says:

errrr.... you do realize you are using a computer to do this right? Not just posting to YouTube, but the camera you used to capture the images and the output monitors.

And since all of these things run on types of algorithms, it should not be surprising that these sorts of things show up. Recursion is a sort of shortcut, and repeatedly feeding the same information over and over would tend to clump it into patterns.

Just sayin'

• Jodo Kast says:

Troll, you miss the point.

• [...] Como hacer fractales sin un ordenador   scientopia.org/blogs/goodmath/2010/11/02/fractals-without...  por nofacefarmer hace 3 segundos [...]

• fag says:

Why do think this isnt digital?

• Ping says:

I saw this at a science exhibit when I was a little kid... I think it was the Ontario Science Centre in the 1980s. They didn't have projectors; it was a camera pointed at a TV screen with mirrors around it. It was extremely cool.

• John D. says:

I don't know if 3 monitors would work as well as three projectors--it may be that the overlap is a required feature.
But projectors these days are so common that they even show up as children's toys, like the Eyeclops version:

Findable at \$40-\$60 each, so almost worth wasting the money for 3 at a time.

• Stewart Hinsley says:

It seems to me that what this generates is (an approximation to) an attractor of an iterated function system. To the best of my knowledge Julia fractals don't come into that category.

• jofr says:

That's cool, producing Iterated Functions Systems (IFS) with multiple projectors or displays. Fractals are always amazing!

• Keith Harwood says:

The general phenomenom was known from the earliest days of television, when it was known as howl-around (after the similar audio effect). The original title sequence for Dr. Who was made this way and that was in 1963, so no computers in the path at all.

First thing I did when I got a video camera was point it at the TV screen to amuse my children. Still no computer in the path.

• [...] pattern. Usually the fractals are calculated with a computer, but is is possible to produce Fractals without a Computer! It’s very cool – partly because it looks neat, but also partly because it shows you [...]

• Scientopia Blogs