Art with a Mathematical Twist

Euler points out a story about art created through mathematics. The Science News article covers selections from a recent exhibit, where over 40 artists gathered to show their work and the math behind it. The rest of the pieces are also viewable at the exhibit's website. "Michael Field, a mathematics professor at the University of Houston, finds artistic inspiration in his work on dynamical systems. A mathematical dynamical system is just any rule that determines how a point moves around a plane. Field uses an equation that takes any point on a piece of paper and moves it to a different spot. Field repeats this process over and over again--around 5 billion times--and keeps track of how often each pixel-sized spot in the plane gets landed on. The more often a pixel gets hit, the deeper the shade Field colors it."

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Doesn't most art have a mathematical twist?

[pipoca]

If you have the photorealism of the Rennaisance, you get all of the math involved in regular life (e.g. the golden ratio). With various less realistic artists (e.g. Pollock, Van Gogh), haven't mathematicians found various deep mathematical patterns in their work? This is what you get when you start out with pure math, and turn it into art, whereas most of art is what you get when you have an intuitive understanding of math (i.e. what looks good) and go with that. All art has math in it.

Mathematical Music

[ilikepi314]

What I found more interesting than mathematical art was the music produced from differential equations and such.

I really wish I remember more details but a few years ago I saw a presentation by a mathematician in which he had a little program that solved some sort of equations. Grr, I'm going to hate myself now for not remembering. Well, regardless the details, it solved something and assigned the solution values specific notes/chords from a piano, so that whenever a value was obtained, the computer played that note. Thus, the time evolution gave a sequence of notes, and so he recorded this sequence.

He played a few excerpts, I tell you what, it sounded like Mozart or Beethoven. Well, certain parts you could pick up a very forced/electronic feel to it, but other parts glided so beautifully that it sounded like a master pianist was playing.

That was an incredible lecture. Perhaps anyone else knows what I speak of? I'd like to find out what program and equations were used, it was fascinating.

This is the only kind of art I can do

[MillionthMonkey]

A few years ago I got the idea to write code that fed massive scene files into POV-Ray. There are probably better tools nowadays but POV-Ray had the virtue of a simple scene description language that I was already familiar with. It's easy to create code to generate it.

I made a heart out of the sextic (huhhuhhuhhuh) polynomial

(2xx+2yy+zz-1)^3 - xxzzz/10 - yyzzz = 0

and had POV-Ray create a bunch of scene files by rotating this thing through 180 degrees to create an animated heart GIF. [photobucket.com] (This was back in the Dark Ages when the web was full of animated GIFs.) There were probably a thousand other animated hearts out there but this one was mine.

I got the idea to do space filling of the unit sphere with thousands and thousands of small boxes [photobucket.com] or smaller spheres, [photobucket.com] playing around with the lighting to see if I could create something vaguely moonlike [photobucket.com] with inside-out craters. I tried doing this with thousands of hearts [photobucket.com] but got bitten in the ass by a bug in POV-Ray's polynomial rendering code where it trips over a planar singularity in the heart equation, so every little heart ends up with an unromantic slit running across its equator. There were just too many to fix by hand.

The most interesting image from this technique came from a routine that recursively generated spheres, invoking itself six times per sphere to create smaller spheres on the top, bottom, left, right, front, and back, each of which then does the same thing, to a depth of 5 or 6. You end up with a Sierpinski octahedron. [photobucket.com]

All this stuff has been done to death by others. I wish I were good at drawing comics.

Re:Sometimes math is created through the arts

[opec]

I'm a musician and nerd, so I had to look up Norgard. Those crazy Danish, I found out that his name is fully Nørgard. Lucky me, I'm sitting working at the library and my search tells me we have recordings of his in the collection. Sweet. Fractal art is good stuff.

Roman Verostko

[raddan]

Roman Verostko and others have been doing something he calls algorithmic art [verostko.com] for awhile. E.g., put a paintbrush in a pen plotter and then write an algorithm to paint on canvas. Although sometimes I feel like artists like Verostko (who call themselves algorists) are tremendously arrogant sometimes (which I suppose makes them like many other artists), a lot of their stuff seems really beautiful to me. In particular, Verostko's pseudo-calligraphy is just mesmerizing to me-- it looks sort of like a written language, but it's not.

And of course, you can't forget the grandmaster of algorithmic art: Bach. Bach was a master of counterpoint, and the mathematical beauty of some of his works (e.g., The Art of Fugue) is readily apparent. If he indeed did not generate his works in an algorithmic way, well, that's surprising to me. Listen to Glenn Could play Bach, Partitas 1,2, and 3 [amazon.com] being my favorite...

procedural art

[vesabios]

I did some mart art work awhile ago, based on Daubechies' scaling functions. Check it out: The Strangers Series [smason.com].

Re:Sometimes math is created through the arts

[Coryoth]

For an interesting take on mathematical analysis of music, you could try The Topos of Music [amazon.com]. It sets out to apply deep modern mathematics to issues of musical composition. Starting with a base in category theory and topos theory (hence the title), it can then spiral down to using differential geometry and algebraic geometry. Personally I don't know enough music theory to know if it really stacks up, but it is certainly mathematically very interesting (and goes well beyond the basic mathematical dabbling of some approaches to bringing math into music that I've seen).

Re:Sometimes math is created through the arts

[popmaker]

But what's the point? Is it achivement in itself to make use of mathematics in music? I would think that the real justification for the whole thing was musical value, not mathematical. The whole idea should be that by bringing mathematics to music, you would be able to create music that sounds truly fascinating, but it sound from you that being able to use the mathematics at all is enough.

I am a little skeptic about bringing mathematics to music - sometimes it seems to be the end in itself, which it shouldn't be. But on the other hand, if the results are MUSICALLY interesting, that's another story. Like the mathematical construction of a truly bizarre polyrhythm. But that still doesn't go beyond simple modular arithmetic.

Some mathematical stuff in music just sounds superficial... like (actual) the idea of writing a piece which shifts the tempo with a ratio of pi : e. You might think it's cool, I don't know, but no one really cares if the ratio is pi : e or 1.2 or "just slightly faster". There is no intrinsic musical value in the idea. So... is it really worth it?