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."

Some great examples of mathematical art

[paroneayea]

If you're interested in pretty, shiny, mathematical things that you can run on Linux, check out:
  - electricsheep: animated fractal flames: http://www.electricsheep.org/ [electricsheep.org] (I highly recommend running this as your screensaver, though it takes a bit for the first sheep to download)
  - Jenn: pretty, shiny, blue(?) polytopes, rendered on your computer: http://www.math.cmu.edu/~fho/jenn/ [cmu.edu]

Anyone have any others?

IFS, fractal flames

[Anonymous Coward]

The images described in the summary (which are not really representative of most of the stuff in the gallery, just Fields's stuff) are generally known as iterated function systems [wikipedia.org], and perhaps belong to the subset known as fractal flames. The description is fairly accurate, but the images he has made are rather unimpressive compared to ones I've seen (and made myself). Probably the best known example of a fractal flame program is Electric Sheep [electricsheep.org]. However, another good program for making fractal flames is called Apophysis [sourceforge.net] (regretfully, it's Windows only, but does work fairly well under Wine). I've been working with Apophysis for about 3 years now, and trust me, there's a lot of more artistic stuff out there that uses fractal flames. Even some of the stuff on Wikimedia Commons [wikimedia.org] is better than his stuff.

Coincidentally, my captcha was "artful".

Re:Some great examples of mathematical art

[baud123]

You can play with k3dsurf http://k3dsurf.sourceforge.net/index.html [sourceforge.net] and have a look at inspirations it gave http://www.evolution-of-genius.de/3d/ [evolution-of-genius.de] The rendering is very good in 3D

New and yet not new

[fractalus]

It's true that mathematical proportions and structures have been found in artwork for centuries, but what's different about these things is the role of the algorithm and raw computational power in producing this artwork. These are works that could not have been done before the availability of computers. The artist directs and controls the mathematics, using them like other artists use different kinds of paints, brushes, and canvas. But the computer does the mind-numbingly tedious work of billions of computations to render it on-screen. This is not all that different from artists using 3D sculpting and rendering tools; it's just a different set of algorithms.

Others have pointed out Electric Sheep and Apophysis; these focus on one particular type of non-linear iterated function system, the "fractal flame". There are many other fractal rendering tools out there, some free, some not. Wikipedia has a list if you're interested. This is a medium that has been in constant change for twenty years and doesn't look like it's ready to settle down any time soon.

Context Free

[replicant108]

Context Free is a program that generates images from written instructions called a grammar. The program follows the instructions in a few seconds to create images that can contain millions of shapes. The program itself is GPLed and available here [contextfreeart.org].

As you can see from the link below, some of the results from this project are stunning.

Context Free Art gallery [contextfreeart.org].

Re:Some great examples of mathematical art

[maxume]

http://www.chaoscope.org/ [chaoscope.org]

via:

http://nedbatchelder.com/blog/200705/chaoscope.html [nedbatchelder.com]

he also mentioned Jenn:

http://nedbatchelder.com/blog/200802/jenn_visualizing_polytopes.html [nedbatchelder.com]

Re:Mathematical Music

[Ambitwistor]

You might find it somewhere in Wikipedia's computer generated music [wikipedia.org] article.

Processing

[mingrassia]

>> Anyone have any others?

Perhaps the king of all environments (at least in my mind) is Processing [processing.org]. It is a Java based environment created by Ben Fry [benfry.com] and Casey Reas [reas.com]. It's open source, has a huge active community [processing.org], and plenty of 3rd party libraries [processing.org] for exploring things like computer vision, audio, physics, ray tracing, AI, etc.

There are a ton of really talented people doing cool things in Processing. Too many to list here, check out the Exhibition [processing.org] page for things to play around with.

Escher

[Anonymous Coward]

How can this thread go on this long without the obvious comment about MC Escher's hyperbolic tilings (such as the Circle Limit images)? It's not like there wasn't a world renowned mathematician (H. S. M. Coxeter) helping him work out the details... (and let's not forgot some of the inspiration he also got from Roger Penrose and his father L. S. Penrose)

Re:Roman Verostko

[theazreal]

Fugues are inherently algorithmic. You take a theme, invert, reserve, invert-reverse, modulate... Bach just did this in a particularly beautiful and inventive way. You'll find his counterpoint and stretto are also somewhat regular. http://en.wikipedia.org/wiki/Fugue [wikipedia.org]