"Coral Star" shows the motion brought about by one particular dynamical system.
Michael Field
Posted on 02/20/2008 11:18:56 PM PST by neverdem
Mathematicians often rhapsodize about the austere elegance of a well-wrought proof. But math also has a simpler sort of beauty that is perhaps easier to appreciate: It can be used to create objects that are just plain pretty—and fascinating to boot.
That beauty was richly on display at an exhibition of mathematical art at the Joint Mathematics Meetings in San Diego in January, where more than 40 artists showed their creations.
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.
The reason mathematicians are so fascinated by dynamical systems is that very simple equations can produce very complicated behavior. Field has found that such complex behavior can create some beautiful images. For example, the dynamical system he depicts in "Coral Star" does some peculiar things as it gets closer to the center (technically, the equation is discontinuous at the origin). So as you get closer and closer to the center, the image gets more and more complex.
"Even apart from the center, the image has quite a lot of depth to it," Field says. "It's a feature of the way it's colored. I'm not so keen on bright primary colors. The shading makes it more interesting."
This image has an unusual 35-fold symmetry, and Field created it as a present for his wife on...
(Excerpt) Read more at sciencenews.org ...
Mandelbrot Sets can create pretty interesting patterns too.
Bivariate normal distribution, boring.
For some reason, I’ve always had the nagging notion that there must be some deeper significance to this beauty and complexity lurking in simple mathematical expressions.
It just seems like it has to mean something.
I may not know anything about art but I know it when I see it. If it’s pretty, it’s art, right?
Is that true for all of the pics at the Science News article, or just "Coral Star"?
Anyone with a decent PC can get started making their own fractal art and video nowadays.
I think that the Escher thing is pretty cool, but I left it in the attic, so I will have to go in the basement and look.
If that made any sense to anyone. I am up way too late - this broken leg is kicking my butt.
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In other words -- a spirograph.
Now that is a cool design - but is it livable?
Soviet blocks kill the spirit.
Unless you're a liberal, in which case it's art if it's ugly!
Wow! Thanks for posting. I’ve bookmarked his site.
Makes sense - Another World, Ascending and Descending, Belvedere, Concave and Convex, Cycles, High and Low, House of Stairs, Print Gallery, Relativity, Up and Down, Waterfall...
There will always be difficulties in depicting 3 dimensional(tri-nomial) drawings on a 2 dimensional plane(bi-nomial). When you add time to the equation it gets even more difficult. What appears to be chaos actually has order.
Make your own with'Apophysis'.
Isn’t this the same thing as visual MUZAK?
That top (leaf) pattern is stunning. Thanks for posting.
Muzak is relatively simple auditory aesthetics but far more complex than these relatively simple visual ones.
Or if it's ugly it is art.
Here are some galleries:
http://flam3.com/index.cgi?&menu=galleries
Here’s a link to download the program:
http://www.apophysis.org/
Other similar programs are available.
In which case Hillary should be in the Louvre.
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