I Attempt Feedback

As I mentioned in my last post, I'm working on a visual accompaniment to a piece of music, consisting entirely of images generated by video feedback. I've done this a couple of times before, but that was in the 1970's; since then I've played with feedback occasionally but not tried to do anything serious with it. The simplest form of video feedback involves pointing a camera at a screen displaying the output of the camera. Because there is a one-frame delay from when a pixel on the screen changes until that change is sent back to the screen from the camera, a delayed feedback loop is created. Here's a still photo taken off a video of the basic setup:

Now you can move, tilt, and zoom the camera to make some more interesting patterns:

Note the camera control icons in these stills. I don't have a video camcorder, so I tried to use the video mode of a point and shoot digital camera. In fact, I tried 2 different cameras, and found that I couldn't get rid of all the icons on either of them. My current budget is constrained enough that I can't afford to go out and buy a camcorder just now, so simple video feedback is problematic for this project.

Never fear, the computer will save me. Turns out it's not at all difficult to simulate video feedback with a program. On Mac OS X, there is a program called Quartz Composer that allows you to program complicated video effects in the Core Image API. You can build components (called "patches") for these programs using standard Mac Objective-C coding, but once they're built, you can wire them together with composer in a visual editor paradigm. Since the system comes supplied with a wide-range of patches, and there are more at various developer sites on the web, you can do a lot without ever writing any code. I made some simple feedback videos using input from the iSight camera in my laptop feeding into Quartz Composer; here's one still:

Here's a screen-shot of a composer editor window:

That window shows the wiring diagram for a feedback video that looks like this:

And here's a short video of another simulated feedback program:

I'm now working on the problem of getting the clips of simulated feedback into my movie editing software so I can cut them to the music. For some reason one of them worked, but the second one I tried can't be imported correctly. Oh, the joys of software! I'll post more on this subject as I make progress.

Art with Numbers

It may surprise some people that there are a lot of connections between mathematics and visual art¹, it might surprise you to know that the field of Mathematical Art has flowered in the last decade as never before.  Part of the reason for this flowering is that an earlier generation of artists such as M. C. Escher  and mathematicians like H. S. M. Coxeter and Roger Penrose created an environment in which mathematicians and artists could publicly discuss each others' work.  Part of the reason is the relentless application of Moore's Law to the tasks of computing and displaying shape, color, and texture².  And part of the reason is the application of computers and computer-controlled tools to the creation of artwork.  That last part has largely been involved with the creation of sculpture, from the 3D printing of jewelry by Bathsheba Grossman to the creation of monumental sculpture with CNC machine tools by Helaman Ferguson.

Most of the mathematical art produced in the last few years has been in the form of computer graphic images (it's become cheap and easy with available software), but other media are popular too.  I've already mentioned 3D printing and machining, and there has been a lot of work in various textile media such as quilting, chrocheting, and embroidery, and origami has been claimed as a field of mathematics.  There's been work in more evanescent forms such as soap bubbles and light shows⁴.

One obvious source of inspiration for artists is geometry, plane or solid, Euclidian, spherical or hyperbolic.  Escher created many beautiful examples of all of those categories.  But there are many other areas of mathematics which have a visual aspect that lends itself to implementation by the artist: topology, dynamic systems theory, packing theory, and so on³.  Recently nearly 20 years of work by a loose cooperative of mathematical artists (or is that artistic mathematicians) including the science fiction writer Rudy Rucker, ended in the discovery of a 3 dimensional analog of the Mandelbrot set and the creation of some really beautiful images.

If all this sounds interesting, you can follow the link in the title of this post to a site of links to a number of artists working with mathematical images of all sorts.  I plan to blog more on this subject, and say more about specific artists.  To get you started on some of the do-it-yourself possibilities, here's a miscellany of books and links.  Some of the books, especially the ones on theory, are rather expensive, but you can find them at many public or university libraries.  The book links are to bookdepository.com.

General books on Mathematical Art:
"Fragments of Infinity: A Kaleidoscope of Math and: A Kaleidoscope of Mathematics and Art" by Ivars Peterson

Theory or Mathematical Art:
"The Visual Mind II" by Michelle Emmer
"M. C. Escher's Legacy" by Doris Schattschneider

Textile work:
The Home of Mathematical Knitting (sarah-marie's mathematical knitting pages)

"Making Mathematics with Needlework" edited by Sarah-Marie Belcastro and Carolyn Yackel
"Curve Stitching: Art of Sewing Beautiful Mathematical Patterns" by Jon Millington

Software:
The Geometry Center Download Page

¹ It certainly won't surprise any artists who took a course in perspective drawing.
² I wonder just what percentage of the world's CPU cycles has been involved with displaying some part of the Mandelbrot set.
³ For more than a century a war has been waged within mathematics over the legitimacy and relative importance of visual intuition in mathematical research and understanding.  Coxeter fought for many years for the use of diagrams and visual insight, often against the hydra-headed Nicolas Bourbaki.  Both art and mathematics were the benefactors of that battle.
⁴ There is a group in Germany that projects light shows onto buildings.