I recently returned from a 10-day trip to Hungary that included a brief stay in Budapest followed by a visit to the southern Hungarian city of Pécs (pronounced variously like “Peach”, “Paych”, or “Paysch”). Aside from making a nice vacation to a place I’d never visited before, the purpose of the trip was to attend Bridges 2010, a conference that “brings together practicing mathematicians, scientists, artists, educators, musicians, writers, computer scientists, sculptors, dancers, weavers, and model builders in a lively atmosphere of exchange and mutual encouragement.” I’ll keep this blog post focused on the conference, but hope to eventually add some more information about the rest of my trip.
This was my first time attending the Bridges conference and I only learned about the gathering a few months ago while randomly searching the web for something or another related to art (tessellations, I think). One of the more interesting subtexts throughout the conference, though seldom explicitly part of the presentations, were the ideas of “What is art?” or “Is that art mathematical?” So, a painter who was fully engaged in the art world might look at a visual representation of some complex mathematical construct and wonder if the computer-generated image “counts” as art. On the other hand, some of those more focused on the mathematical side of things wondered whether paintings or photographs that aren’t explicitly based upon equations of some sort were appropriate for the conference. Fortunately, most of the crowd seemed to be open-minded about and interested in both art and math — thus the apropos appellation “Bridges”.
The best of the talks (formal paper presentations) were fascinating and stimulating and had me writing down topics to explore in the future, tools to track down, and ideas for further reflection. I’ll highlight a few of the talks here.
Early on the first day, Christopher Carlson kicked things off with an excellent presentation about using the powerful tool Mathematica to interactively explore visual designs such as for corporate logos. Recently, I had been thinking about Douglas Hofstadter’s ideas about “knob-twiddling”, where he says that, “Making variations on a theme is really the crux of creativity.” (Hofstadter, 1985) Carlson’s talk was a perfect example of “knob-twiddling as creativity”. He starts with a basic logo modeled in Mathematica (a tool that he made look incredibly simple), figures out what the “knobs” should be (i.e., how to parametrize the logo), and then starts twiddling. If you pick the right knobs, you end up with an incredibly powerful way to explore a visual space of logos and find things that would probably have been too difficult to design from scratch.
Later in the morning, Joel Varland, a professor at Savannah College of Art and Design, summoned another author whose work I’m fond of, Mihaly Csikszentmihalyi, in talking about “flow” in math and the arts. Flow, as described by M.C., is the mental state you obtain when working with focus on activities requiring both high skill level and a high degree of challenge. When I’m working on my paintings and things are going well, this is the state where time flies and you’re completely absorbed in the work. Varland explored some of the more literal definitions of flow as they relate to the arts, such as in the dynamics of lines, gestures, and composition.
Craig Kaplan gave a talk about Parquet Deformations, another topic made popular by Douglas Hofstadter. Parquet Deformations depict a kind of metamorphosis (a la M.C. Escher) where a tiled pattern varies slowly across space into a different pattern. They’re fun to look at, hard to draw manually, and Kaplan explained the tools he’s built to help explore the possibilities (more knob-twiddling!).
On the second morning of the conference, Bih-yaw Jin from National Taiwan University explained how he and his students were able to string together some beautiful molecular structures out of ordinary beads. Focusing on “fullerene” structures (roughly spherical carbon molecules), he explained how by looking at the “sprial code” of a particular molecule, you can learn how to string the beads together such that each bead only needs to be “strung” twice to construct sturdy models. In his constructions, the beads represent bonds between atoms, not the atoms themselves. I was fortunate enough to be one of the early birds to his talk and received one of his sample C80 molecules, which has inspired my wife to explore bead stringing designs herself!
In several of my paintings, I’ve used a procedure that I developed in Photoshop to take an image and abstract it into what I found to be pleasing patterns of interacting positive and negative shapes. It wasn’t until Jonathan Mccabe’s presentation, though, that I learned that these patterns have been around for a long time and were in fact discovered by Alan Turing, one of the fathers of computer science. (Excitement: Turing found the same thing I did! Dismay: It’s been around forever and is apparently well known, though not by me!) Turing described a “morphogenesis” process in terms of chemical producers and consumers and hypothesized that this sort of process could be the cause of zebra stripes. Mccabe explains his model for generating Turing patterns by simulating the activator and inhibitor dynamics in a randomized grayscale image, and then shows how he can use Turing patterns at multiple scales within the same image to create complex, dynamic, beautifully biological artistic images.
A few of my paintings that include Turing patterns:
Artist James Mai gave a talk about simultaneous color contrast which started with “color theory 101” but then moved on to his own work, paintings that are specifically about the interaction of colors and the ways in which adjacent colors affect each other in our perceptions.
On “Hungarian Day”, István Orosz explained the motivation and technique behind his double meaning and anamorphic artwork. In work such as “Durer in the Forest”, Orosz places one image within another, often “hiding” (in plain sight) a portrait of a person that the rest of the image relates to. In his anamorphic work, a geometrically distorted image is constructed on a flat surface so that when it is viewed as a reflection in a mirrored cylinder, the “correct” image pops into place. In the best of his pieces, such as in “The Raven (Edgar Allen Poe)”, the anamorphoses are composed so carefully that the image has two meanings, working well without the mirror as one image and then revealing another meaning once the mirror is in place.
Later in the day, Ernő Rubik must have been feeling the love from the crowd and he received the full celebrity treatment in giving a talk about the phenomenon of the Rubik’s cube. With cameras flashing left and right, Rubik explained (in English, for which he apologized that he wasn’t as lyrical as he would be in Hungarian) how he struggled against those who thought the cube couldn’t be successful because it was too hard. The allure of the cube was through its combination of simplicity of concept with complexity of solution, and its TV-friendliness hit the sweet spot of 80s culture at exactly the right time.
The fourth day of the conference was “Excursion Day”. First up were the Vasarely and Zsolnay ceramics museums in Pécs. Vasarely is one of the fathers of Op Art and the museum provides examples of his work from throughout his life. (My wife and I also visited another Vasarely museum in Budapest, but that one was a bit of a disappointment as the lighting was poor and the lady at the front desk tried to rip us off while buying tickets; if I’m generous I’d say she was just bad at math, but realistically it felt like she was trying to take advantage of tourists not familiar with Hungarian language or currency… Fortunately, mathematics is universal and subtraction is simple and we paid the correct amount.) The Pecs museum lights many of the works with perfectly aligned track lighting that makes the paintings appear to glow from within. This large, flat tapestry appeared to bulge out of the wall.
After the museums, we took a trip out to the town of Villány for lunch and a wine-tasting, followed by a visit to a local sculpture garden.
On the final day of the conference, Henry Segerman gave a short talk that explained the causes of some interesting artifacts (e.g., the spokes and rings) that occur when you color in a “sunflower spiral” according to a Fibonacci-related metric.
A few months ago I finished a painting that also made use of a similar sunflower spiral in its underlying composition (which coincidentally had a similar color palette).
Nearing the end of the 5-day conference, David Reimann spoke about using Bézier curves to create interesting tilings based upon Truchet tiles. For the non-mathematicians reading this, a Bézier curve is a way to draw smooth, continuous curves (Wikipedia has excellent animations). Truchet tiles are squares divided into two triangles (e.g., one black and one white), which when laid out in a grid and rotated in various combinations produce pleasing patterns. A variation uses two curves from midpoint-to-midpoint rather than a diagonal line to divide up each square. Reimann showed how using various curves (with both one arc and two arcs per side) on tilings can create aesthetically appealing patterns (reminding me of Brice Marden paintings). This talk had me thinking about my painting, Conceptual Framework, which has a tiling of curves very similar to those of Truchet tiles.
There were many other talks, but these were the ones that I found most interesting and relevant to my own art.