Art, fractal and otherwise

Need a little visual diversion? How about some art with a scientific and mathematical angle – fractal art?

Painting by numbers

[N]ature abounds with examples of fractals: branching rivers and blood vessels, swirling cloud systems, the repeating patterns of mountain ranges and the rocks that comprise them.

People have long looked at these patterns and been fascinated, but it was not until the 1960s, when computers became sufficiently powerful, that mathematicians, scientists and engineers began to create and investigate fractals in their infinite detail.

It's been a fruitful endeavor. Fractal science allows researchers to perceive order in apparent disorder. Fractal concepts have been used to analyze the distribution of galaxies in the universe, the frequencies of economic cycle indices and the probabilities of earthquakes and wildfires.

If you're just interested in some relevant links, the article offers some for a couple of fractal artists: Kerry Mitchell and Janet Parke.

Art and science/mathematics get along very well, I think, as I sort of suggested not long ago.

Bathsheba Grossman's art mentioned in that recent post is not purely mechanical in the way (some) fractal art is, in that the latter may be (though it isn't always) generated purely by computer algorithms. Grossman's work, as with some fractal art, exhibits imaginative human intervention in a number of ways. And the same can be said of other forms of expression now regarded as "art" with little dispute, such as photography.

Even when the subject of a photograph is captured purely mechanically by a camera and reproduced mostly mechanically, the artist's creative intervention is still involved in various ways, such as choice of subject, waiting for the "decisive moment", cropping of an image in the camera or afterwards, lighting, and so forth. And that's before indisputably creative activity in manipulation of photographic images in the printing process or (more recently) by digital means.

But let's consider fractal art that consists purely of the execution of a computer algorithm. Is that still art? I think it can be, because the "creator" of such a work still chooses the algorithms, the initial inputs, and various parameters of the algorithm.

Still, some people may question whether it's art. Now, I don't feel a need to change anyone's mind about that, since art is still ultimately something perceived in the mind of the beholder. If it doesn't work for you as "art", then it ain't art – for you.

Caution: beyond this point I'm just going to ramble a bit, without any pretense of being rigorous or scientific. If you have little patience for that sort of thing, you can cease and desist reading right here.

I recently witnessed an online discussion among intelligent people about the ancient question of "what is art?" Though I refrained from joining that discussion, there were some points raised, which probably always are in this sort of discussion, and which I wanted to reply to. So I'll do it now.

One point is the assertion that "art must communicate some message". But that assertion can lead to further questions. For instance, can we analyze such communication in an information theoretic way, à la Claude Shannon? And what is a "message" in the first place?

People with a scientific or engineering bent are particularly wont to attempt such an analysis, but I have my doubts about that approach. I would simply ask, what is the message, if any, that is communicated in a work by someone like Jackson Pollack? I don't know. Perhaps someone could contrive to find a message in a Pollack painting.

But that doesn't seem necessary to me. I can still enjoy a Pollack painting because it engages and stimulates my visual sensory apparatus, and it is "good" art because the pleasure of the stimulation it provides doesn't quickly become tiresome and lose its ability to engage. To this way of thinking, some of the better examples of fractal art (at least) also deserve to be called art, even if no specific "message" is communicated.

Another problem with the idea of "message" and "communication" being present in a proper work of art is the subject of much "postmodern" analysis of art, and in particular the "deconstruction" of a work of art. There's no way I can possibly do justice to this point of view in the space of a few paragraphs – people write long, convoluted books about such things. Nevertheless, my understanding of this idea, sketchy as it may be, is that postmodernism argues against inherent "meaning" in a cultural artifact, because most of the "meaning" actually depends on cultural context that the artifact implicitly references. And "deconstruction" of a work of art (or of other cultural artifacts like "messages" and "narratives") is the process of making explicit the cultural frames, assumptions, context, abstractions, metaphors, categories, etc., to which the artifact makes allusion, and without which the artifact cannot be understood or said to have any particular meaning at all.

A fine example, it seems to me, would be the Cycladic statues, such as have just been in the news on account of recent excavations, though many instances have long been known. The news article explains

The Cycladic culture — a network of small, sometimes fortified farming and fishing settlements that traded with mainland Greece, Crete and Asia Minor — is best known for the elegant figurines: mostly naked, elongated figures with arms folded under their chests. It flourished in 3200-2000 B.C.[E.], then was eclipsed by Crete and Mycenaean Greece.

But in spite of this antiquity, the figures seem like very modern abstract art and appeal to modern artistic sensibilities. Yet we know almost nothing about the culture in which the figures were created, and have very little idea of what they "meant" to people of that culture.

The figurines were made following a pattern that changed little over 800 years. They have been variously interpreted as depicting gods or venerated ancestors, serving as replacements for human sacrifice, grave goods — even children's toys.

Might we say, then, that art can be appreciated even if we don't know what a piece of art "means", even if it doesn't have an invariant, unambiguous meaning? And further, that what's important in art – whether it be fractal forms, Jackson Pollack paintings, Ansel Adams photos, or Cycladic statues – is its ability to capture our attention (at least for awhile) and to "entertain" us and our senses?

Indeed, as I'm writing this, I'm also listening to some Beethoven piano sonatas. Music is certainly an example of a type of art which is primarily appreciated, without apology, as a form of entertainment, sensual gratification. (Even though it is well recognized that there is a such a thing as "program music", in contrast to "absolute music".) This is as true of Beethoven's music as it is of the music of the recently deceased James Brown (about whom and whose music I know essentially nothing).

Fine. Now having said all that, I'm going to reverse direction and consider the opposite point of view: art as message. In the first place, there's a lot of art (or what is asserted by some to be art) which is not entirely pleasing either to the senses or to the reflective mind. For example, novels of Dostoevsky or Kafka, or paintings by Pablo Picasso (Guernica) or Francisco Goya (The Third of May). Zillions of other examples could be cited, many of which might rather more likely be described as "disturbing" or "emetic", rather than as "entertaining" or "pleasing". About the only thing that could be described as pleasing about such works is the intellectual pleasure of grasping their message. That's certainly a valid kind of pleasure, but still...

A particular type of art in this category came up in the discussion mentioned previously. Or rather two related types: found art and performance art. An early example of found art is Marcel Duchamp's Fountain – a urinal. Examples of performance art can be found in the work of Karen Finley, involving (according to Wikipedia) "graphic depictions of sexuality, abuse, and disenfranchisement."

What's "entertaining" about this sort of thing (apart, perhaps, from erotic elements and fetishes)? Well, not necessarily anything, in any customary sense of "entertaining". The art here, if any, resides in its message. But many people assert that they can scarcely, if at all, see any real message. The example cited in discussion, if I recall correctly, was a load of trash dumped on the lawn before a civic building. "You call that art?" many people ask rhetorically.

Well, yes, as a matter of fact, provided one allows as art artifacts or performances which use at least some modicum of imagination to convey a message. What I would say is that in many cases people don't recognize the message because they don't like the message, though they in fact perceive it subliminally at some level. Further, a difficulty in perceiving the message results when the viewer does not share much of the artist's conceptual framework. In other words, as postmodernists point out, most or all of the meaning of an artifact or performance resides in its cultural context, categories, allusions, etc.

Just as one can't appreciate a novel written in a language one doesn't know, one can't (fully) appreciate a nonverbal artifact if one doesn't know all the concepts and associations that the artifact embodies for the artist. Communication can't effectively occur unless there is a sufficient amount of shared conceptual space. (Try explaining diffeomorphisms to someone who doesn't even know calculus.) And communication must occur for art of the "message" sort to be worthwhile – as opposed to art of the "sensory" sort which appeals directly to the human perceptual apparatus in one or more modalities.

Regarding message art, I've coined an aphorism which, as far as I know, is original. "Art is how we try to explain us to ourselves." Here, "us" could be humans in general, or a specific cultural group. Obviously, this applies mostly to art as a form of communication. When people disagree with this, I take it that they are thinking of more sensory kinds of art. Or perhaps, simply recognizing that message art doesn't always articulate answers and explanatations – sometimes only nagging questions. (Note to self: some other time go into the etymology of words like articulate, artifact, artifice, artificial, etc.)

Time to wrap up. People disagree about what is or is not art because there are acually two rather different things that people can talk about in the category of art. These two things are analogous to what in musicology is called program music vs. what is called absolute music.

This isn't an especially deep or profound observation. In terms of neurobiology, all we're talking about is stuff that goes on in the frontal cortex and other regions that support cognitive functions vs. the stuff that goes on in perceptual regions (e. g. parietal and occipital lobes) and supporting regions that mediate emotions, like the amygdalae.

After all, this is a science blog, so you knew the discussion had to come down to physical realities eventually, didn't you? Nobody here but us reductionists, boss.

Note: This might be a topic to get some good comments on. So if anything I've said here touches a nerve, feel free to comment away.

Tags: art, fractals, neurobiology, postmodernism, deconstruction, Cycladic sculpture