Monday, October 20, 2008

Pierre de Fermat

Malcolm Gladwell writes in the October 20, 2008, New Yorker, that in our accounting of creativity we have forgotten to make sense of late bloomers. We expect poets, artists, and mathematicians to do their best work before middle age. We tend to accept the conventional wisdom that age is the enemy of creativity.

Mathematician Pierre de Fermat (1601–1665) had completed a manuscript for his pioneering work in analytic geometry by the time he was 35, but he also helped lay the groundwork for probability theory when he was 53. Fermat's example contradicts what G. H. Hardy said in his essay, A Mathematician's Apology (full text here):
"No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." G. H. Hardy (1877 – 1947)
Hardy may have been right that original mathematics is the most difficult discipline to continue into middle age and beyond, but Gladwell says something else is going on. Gladwell's article covers the work of University of Chicago economist, David Galenson, who showed that there are two different life cycles of artistic creativity — the conceptual and the experimental. Gladwell writes:
"The Cézannes of the world bloom late not as a result of some defect in character, or distraction, or lack of ambition, but because the kind of creativity that proceeds through trial and error necessarily takes a long time to come to fruition."
Fermat was a lawyer first, and though devoted to mathematics, he never felt the need to publish. His work survives through correspondence and notes he made, rather than finished writings. It seems to me that he chose to be the experimentalist, and wasn't distracted by his own early success. Like Cézanne, Fermat was more interested in the process of discovery, and less distracted by his own success.

I usually end a post with a gratuitous link to some new artwork of mine. In this case, I'm connecting Fermat's spiral, which he discussed in 1636, to the first drawing for a new series — Fermat's Spiral. (More to come. . .)

Sunday, October 19, 2008

Ernst Haeckel

In previous blogs (More. . ., and Artist-Scientist Maria Sibylla Merian. . .) I referred to the artist/naturalist. Here's a link to 100 images by Ernst Haeckel, whose work survives alongside the prints of Maria Sibylla Merian. Here's a link to an exhibit of natural history books by ten authors, including Merian. Here's a link to the work of Richard Hertwig, a scholar of Ernst Haeckel.

Here's just one image of radiolarians from Haeckel's Kunstformen der Natur (Artforms of nature), followed by my own interpretation, "Radiolarian Skeleton."

Friday, October 17, 2008

Alexander Calder

Continuing my search for artists with science or math training, while reading about the Whitney Museum of America Art exhibit "Alexander Calder: The Paris Years, 1926-1933", I discovered that Calder trained as an engineer. Previously, I identified Jess Collins, Jo Baer, Portland artists Julian Voss-Andreae and Stephan Soihl, and the artist and entomologist, Maria Sibylla Merian (1647-1717). Calder went to the Stevens Institute of Technology in New Jersey, and worked for a short time as a hydraulics engineer and a draughtsman for the New York Edison Company.

Surely the other end of the art spectrum from an exhibit at the Whitney would be a gallery show that accepts all entrants and charges a fee. For the time being, I'll have to be content with the later — Snap to Grid 2008, at the Los Angeles Center for Digital Art includes one of my "Canopy" prints.

Wednesday, October 15, 2008


The digital art at is grouped by project. Many of these projects share a common purpose — to extend a graphics system in some new way and thereby provide a tool for creating new imagery. The Rectangles and Spirals project extends features of the golden rectangle to other rectangles by generalizing the golden ratio formula and the Fibonacci number sequence. The Small Programs and Plane Symmetry Groups projects relate to plane symmetry or wallpaper groups, but differ in ways that disqualify them from, while extending the mathematical form.

The Coprimes and Greatest Common Divisor (GCD) projects plot the GCD of integers as colored cells within a grid. Patterns are generated by extending the integers provided to the GCD calculation beyond the grid column and row numbers. These numbers figure in a pair of formulas to generate different GCDs.

I based the Perspectives project on a simple two-point perspective drawing function. Instead of using the tool to create visually accurate perspective drawings I mix several viewpoints within the same drawings.

The Cubes and Cabtaxi Fleet project is based on the recreational math idea of taxicab and cabtaxi numbers. It suggests possibilities for representing the numbers in sculpture.

Here's my latest Small Programs drawing, "Apse". The apse, a frequently vaulted recess at the sanctuary end, may extend the exterior of a church.

Monday, October 13, 2008

Four Similar

Here are four new images from my Small Programs series. They were developed with mostly common code. As usual, I generate the unit cell with a small program. The program randomly varies the resulting pattern. I like to consider this technique an extension of plane symmetry or wallpaper groups in that instead of translating, rotating, or reflecting the primitive cell, the small program regenerates a varying image each cell. This gives me control over the total image. For example, I did a series of three entitled "Lessness", I, II and III, with clumped images in the center, in a grid, and along diagonal rows. In the first image below the program generates sparse cells toward the center.

Friday, October 10, 2008

Lessness III

Here's the final drawing of three entitled "Lessness", I, II and III. "Lessness" is a short story by Samuel Beckett in which he randomly ordered the sentences. The Lessness drawings are from my series, Small Programs, which relate to plane symmetry or wallpaper groups except I generate the unit cell with a small program. The program randomly varies the resulting pattern.

Saturday, October 4, 2008

More Art and Science

Last June we went to see the Getty Center exhibition, "Maria Sibylla Merian & Daughters: Women of Art and Science". Merian was an artist and entomologist, with a special talent for natural history illustration and printmaking. I have an interest in artists with scientific or technical backgrounds such as Jess and Jo Baer, or artists that understand how to use technology as well as Larry Bell does. Last night I saw Susan Murrell's exhibit at galleryHomeland, in Portland. Murrell recreates the effect of scientific illustration and museum display without the actual science. She fabricates displays and specimen boxes of fantastic faux creatures. She paints multi-layered abstracts on transparent acetate that hint at purposeful geological renderings and maps. The whole presentation is tied together by call out label leader lines, installation style with tape applied directly to the wall. It's similar to installations and sculpture that reference without being informed by architecture. Eric Zimmerman is one of many young artists taking architecture and doing installations and drawings similar to what Murrell does with biology or geology. (See and Art Lies, Issue 58.)

This forces me to think about my own pursuit of art grounded in math. In my work I use programming, simple math, elementary algebra, trigonometry, and Euclidean geometry. Yet, the closest I've come to actually practicing math was with my project on a generalization of the golden ratio formula. So, what's the point in mimicking, paralleling, or otherwise borrowing from math, science, and architecture to create art? I've noticed that many artists want to separate themselves from the technical. They blatantly use technical imagery while distancing themselves from the technology. Both Robert Mangold and Mel Bochner de-emphasized the math in their art. Susan Murrell takes this much further. Joel Courtney said of Murrell in the 6/20/2008 Las Cruces Bulletin, "Even though science is a large influence, Murrell goes out of her way to avoid studying the sciences further so as not to cloud over the messages of her artwork with the particulars of the technical world." Murrell was quoted, "My ignorance (of natural science) is part of the equation in a way. The abstraction does dumb it down a bit, but it allows my work to explain it to others."

In contrast, I prefer the technical illustration of Merian to the parody. This inspires me to renew my efforts toward taking a stand opposite to mimicry and parody. Merian used artistic talent to advance science. Can we use math or computer science to advance art without trivializing the technical aspect? Mel Bochner said,
"Mathematical thinking is generally considered the antithesis of artistic thinking, but it is not. The two aspects of mathematical thinking that interest me are its clarity and rigor. These are also the characteristics of the best art." Mel Bochner — in his “ICA Lecture”, 1971. [Reprinted in Bochner, Solar System & Rest Rooms, Writings and Interviews, 1965-2007, Cambridge, MA: The MIT Press, ISBN 978-0-262-02631-4. Page 90-92.]
So Bochner seems to say that art should be precise and valid like mathematical thinking, but I think there's much more opportunity here than Bochner's statement implies. I think twentieth century art opened up possibilities for artists to use materials, skills, and techniques from all professions. I hate to see artists stuck within the limitations of pre-twentieth century art simply mimicking other professions when they could employ the techniques and knowledge of those professions to make a new art.

I'm sure there are other artists with a technical background and a portfolio of work that advances rather than parodies science in art. In Portland we have Julian Voss-Andreae who studied physics at the universities of Berlin and Edinburgh and did graduate research in quantum physics. Also, there's Stephan Soihl (B.A. in Physics) of Mt. Hood Community College and Blackfish Gallery. Coincidentally, Soihl also does botanically accurate watercolors.

Here's a second version of a drawing from my Small Programs project.

Friday, October 3, 2008

Magnetic Field

Here's another drawing from my Small Programs project. This image depends heavily on the program's ability to concentrate images toward the center of the grid.

Wednesday, October 1, 2008


An object or a system is called chiral if it differs from its mirror image, that is it cannot be superimposed on its mirror image.

The Small Programs are digital drawings that I program instead of using traditional artist's media. They grew out of my Plane Symmetry Groups project. These drawings relate to plane symmetry or wallpaper groups, but they differ in ways that disqualify them from, while extending the mathematical form. The primitive cell in each of these patterns is generated by a small program. Like plane symmetry groups, I can transform, rotate, or reflect the cell. However, the drawings differ from the mathematical form in that I generate the unit pattern programmatically. I have replaced the static cell with a small program which may randomly vary the resulting unit pattern. The patterns are isosceles trapezoids arranged radially in tracks around a center point. The patterns grow in width as the tracks radiate out.

I explore small programs in somewhat the same way I would use traditional media. I have a general idea of the result I am attempting to achieve before I start coding. I work through various challenges during the process. I selectively discard or keep elements as I approach the final rendering.

The programs are Flash ActionScript. I often use random selection within the program, so the result varies each time an image is rendered.

Here are two new closely related prints in the Small Programs series.

"Prebiotic Earth"

"Mass Ascension"