Van Gogh's Turbulent Period

Starry Starry night,
Vortices swirl around each star,
Eddies within eddies from near and far
With flows that know the darkness in my soul..

OK. Enough Don McClean. This post is about Van Gogh and his uncanny ability to depict reality in an unreal way, raising once again the question: Do certain artists have an ability to capture physical process and /or mathematical truths that can't be mimicked by others? And is there a correlation with this ability and madness?

Where Jackson Pollock's paintings are instantiations of splattered fractals, Van Gogh's paintings have recently been compared to one of the main avatars of chaos theory: turbulence.

Click to read more ...

Art and the Event Horizon Effect

Horizon Event, by Anton SevcikIn a wonderful MASM (meeting of arts and science moment) a few weeks back, Anton (John) Sevcik - an old friend I had not seen in almost 16 - years had an art opening at the Fleisher Art Memorial in Phila. In his show Myth and Landscape, Anton displayed a number of paintings that featured a horizon as part of the story and inspiration for the piece, including one titled Horizon Event.

Anton has read and talked about physics for as long as I've known him. His work is often influenced by the ideas that affect him deeply. In Horizon Event, Anton conflates two ideas - The Event Horizon, and the Horizon Effect.

The event horizon is the boundary of a black hole, a region of space-time from which light cannot escape. Anything passing the horizon will vanish into oblivion.

The Horizon Effect arises from a non-physical situation. This effect is usually used to describe a situation where something that is out of sight - just beyond the horizon - is assumed to either be benign, or not exist. Often the horizon is not a physical one, but rather a demarcation point in a process. Artificial intelligence software, e.g., often suffers from the effect. Using look-ahead trees for decision making (as in, e.g. a chess program), the trees must be truncated at some point, possibly before revealing a fatal error about to occur.

Both event horizon and horizon effect then describe a knowledge/lack of knowledge interface. One is physically defined because of a singularity in spacetime, while the other arises from algorithmic expediency. In both cases there is tension at the boundary between information and chaos, knowledge and incoherence.

Anton's paintings, many of which are dark and brooding (just what is on the other side of that horizon?) suggest a cleft unbridgeable by science but traversable by canvas, oil, and artistic creation.

Anton/John has just started his own blog, View From the Studio, where you'll find more pictures from Myth and Landscape Show.

Eine Kleine Nachtfractal

Listen to Mozart by Renata SpiazziThe melodic recursiveness of most music, especially as manifested in the crystalline, almost-mathematical purity of Mozart compositions, suggests the presence of fractal-like structures that exist both in time and the frequency domain - structures that are both solid and ephemeral, logical and otherworldly.

Some may hear (even if they don't articulate) a richness that is reminiscent of fractal construction. Marin Alsop, Music Director of the Baltimore Symphony Orchestra, describes Mozart's popularity as the result of "the depth of the music and ... the fact that Mozart makes contact with our inner selves. Maybe it's because of his organic approach to composition - taking a small, cellular idea and developing it into something beautiful, he takes you by surprise but also comforts you."

Click to read more ...

Flaming Symmetric Fractals

Apophysis Fractal Flame (click to enlarge)I've seen the flames - fractal flames - and they are amazing. Originally an outgrowth of the ideas developed in Symmetry in Chaos by Field and Golubitsky, fractal flames are related to the Chaos Game because they are created by tracking the iterates of starting points as they are mapped into other points. As in the Chaos Game, the iterates reveal, over time, the structure of the attractor associated with the map. Flame fractals use a combination of non-linear maps and very inventive approaches to coloring/visualization.

Flame mathematics is interesting enough on its own, but the intrigue of flames is the ability to generate images of surreal organic beauty. In the following excerpt from The Fractal Flame Algorithm by Scott Draves for the Cosmic Recursive Fractal Flames site, aesthetics are essential:

Click to read more ...

Tessellatin' Rhythm and Fractal City Maps

Portland - The Fractal (Click to enlarge)One of the craziest art efforts out there is the geospatial art of Nikolas Schiller. Schiller takes satellite photos of cityscapes and melds them into quilts, morphs them onto spherical surfaces, and, basically anything else he can think of. The net result is a set of amazing images of familiar cities looking as if viewed through kaleidoscopes. Many of the images remind me of Escher, only with buildings and landscape features serving as the interlocking escher-figures, receding to infinity at the edges.

Maybe more insane is Schiller's pace: a new map every few days for several years now, all posted on his Daily Render blog, subtitled A Digital Scrapbook for Past, Present, and Future.

Schiller also works with old maps, e.g. combining 16th century maps with current images.

The fractal connection is an obvious one, and Schilling has a special section devoted to images that are more fractal-like. (See the Dupont Circle tessellation, e.g.)

Schiller's motivation is artistic and political. As described in a Washington Post article by D. Montgomery,

Click to read more ...

Mathematics Reveals the Artistry

Brueghel's Fall of IcarusDaniel Rockmore writes about the mathematical analysis of art in the June 2006 Chronicle (The Style of Numbers Behind a Number of Styles). In the essay Rockmore describes Richard Taylor's work in analyzing Jackson Pollock pieces, which may be forgeries. ( See my post on this topic)

The Pollock intro is a lead in to a description of stylometry - the mathematical/scientific analysis of literary texts that attempts to address issues of authorship. (See Bookish Math, an excellent intro to stylometry by Erica Klarreich for Science News Online.) Rockmore than describes a method he developed with co-workers Siwei Lyu and Hany Farid that uses wavelet analysis to determine unique "signatures" of different artists - in effect a stylometry for visual images.

The actual mathematics of the wavelet approach can be found in A Digital Technique for Art Authentication. Here the authors use examples of Pieter Bruegel and Perugino to test their model. They claim that their "techniques, in collaboration with existing physical authentication, to play an important role in the field of art forensics."

The wavelet technique is different from Taylor's fractal analysis of Pollock's works, but both are examples of stylometry applied to visual information. Both Taylor and Rockmore are attempting to quantify art, an activity that Rockmore admits is unsettling/impossible to some. According to Taylor, this quantification should be expected: "Both mathematics and art are all about pattern...it would be unusual that you would not apply mathematical analysis to the question."

Rockmore is more explicit about what mathematical categorization of art analysis does not do: "Fractal analysis doesn't diminish Pollock's athleticism and movement, nature and turbulence, chaos and beauty; it reveals and amplifies it."

For more on this topic, see Can Mathematical Tools Illuminate Artistic Style?, by Sara Robinson for SIAM.

Poetry, Space-time, and Entropy

Plotkin's Entropy by Donna Bellas. See text for info. With the amazing success of Isaacson's bio of Einstein, and the translation and release in the US of Neffe's uniquely-German bio, Einstein is certainly in the air. Not as much as 100 years ago, when he was perhaps the most famous person in the world, but nevertheless many are reading, and writing poetic about Albert.

From Bernhardt Blumenthal, a colleague at La Salle who is a Rilke scholar and poet (and in his spare time chair of the Dept. of Foreign Languages & Literatures and the Master's Program in Central & Eastern European Studies) describes Einstein's influence on his latest work:

...my latest poem, Schwere Seelen, (Heavy Souls), which just appeared last week in a German literary periodical plays on Einstein's General Relativity. The souls, heavy with love and suffering, warp reality and pass over the space-time curve through hyper-space into another universe--one without entropy. The female lover, incidentally, transits space escaping on a light beam exiting a black hole (thus faster than our conventional absolute speed of light) and rescues the beloved from his entropic situation.

Click to read more ...

Imagery in Art and Science - from da Vinci to the Desktop

da Vinci catheterized? See below for details.  Click to enlargeReaders interested in more of the science-art boundary should check out the review by Bettyann Holtzmann Kevles in the May 2007 Scientific American. Titled The Interplay of Art and Science,the piece is an in-depth look at two books by Martin Kemp:

Leonardo da Vinci: Experience, Experiment and Design
and
Seen/Unseen: Art, Science, and Intuition from Leonardo to the Hubble Telescope

(Note: Kemp is a frequent contributor to the Science in Culture column in Nature. A leading expert on da Vinci, he is professor of art history at Oxford.)

According to Kevles, a common theme in both books is how art affects imagery in science and science affects imagery in art, which leads to some very interesting and provocative ideas about digital imagery.

Two parts of the review are of particular interest. In one, Kevles describes how Kemp relates D'Arcy Wentworth Thompson's analysis of the shape and size of living organisms spelled out in his famous work On Growth and Form to the "visual mathematics of fractals, chaos theory and machine-made images."

Continuing with the idea of the connection between visual imagery, art, science, and life, Kevles closes with some of Kemp's concerns about the imagery produced by science (e.g. in the form of medical imaging technology) and the reality behind it. The following is an excerpt: (See Kevles' full review for much more)

Click to read more ...

M.C. Escher: Chaos and Order and Back Again

Order and Chaos. Click to enlarge.

In an earlier post I commented on the ability of M.C. Escher to capture the infinity of time and space in his woodcuts, drawings, and lithographs.

Another common thread in many of Escher's works is the sense of order arising out of chaos - or is it chaos out of order? A master of graphic puns that simultaneously emphasize and blur the demarcation between figure and ground, Escher does seem to lean more in the direction of order out of chaos. In The Magic of M.C. Escher , a fabulous compendium of Escher's works that includes unpublished sketches from his workbooks and excerpts from his correspondence with family and colleagues, this direction is clear:

The consistency of the phenomena around us, order, regularity, cyclical repetitions and renewals, have started to speak to me more and more strongly all the time. The awareness of their presence brings me repose and gives me support. In my pictures I try to bear witness that we are living in a beautiful, ordered world, and not in a chaos without standards, as it sometimes seems.

For a very good intro to a broad selection of Escher's most famous works, visit the M.C. Escher - Life and Work on-line tour at the National Gallery of Art. From the program notes for the Order and Chaos lithograph pictured in this post:

Click to read more ...

The 10th Carnival of Art

Carnival by Elaine Normandy , who uses Gnofract 4D - freeware fractal software for Linux.I found out earlier today that my post on Art and Science Transvergence: Glowing Bunnies was listed in the latest Carnival of Art, a blog carnival that has been hosted by Australian artist Jennie Rosenbaum since June 2006.

I really appreciate the link there - so thank you Jennie!

I urge all readers here to check out Carnival of Art - #10 . With categories in Art History, Art News, Art Philosophy, Artworks, Creating Art, and The Biz, there are a lot of intriguing, compelling, beautiful, and informative posts.

And don't stop there - read the Carnivals of Art #1 through #9.

This is my first experience with a blog carnival, and I am very impressed with the ability to reach more readers, and find more amazing blog posts than I can imagine finding by other routes, including Technorati.

For more on blog carnivals, including how to find them, submit a post, or even host one, check out BlogCarnival.com.

For a detailed analysis of the ability of blog carnivals to be important engines of social networks, and their potential to "become online equivalents of not just TIME magazine, but also GQ, Vogue, Parenting, National Geographic, People, and, why not, Science and Nature" see Blog Carnivals And The Future Of Journalism, an excellent post by Bora Zivkovic in his Science and Politics blog.