Sometimes a mathematical formula can be so perfect, so elegant, those who understand it might call it art. Other times, a mathematical formula actually creates art.
DU mathematics professor Stan Gudder has seen the beauty in math since the 1960s, plugging instructions and formulas into graphics programs to create artwork of startling beauty. His work reflects an otherworldly blend of bright colors, angular lines and perfect arches and curves—all created by variables plugged into complex instructions.
“I really can’t draw, but it is art,” Gudder says. “Instead of a brush, I use a computer.”
While he doesn’t call himself an artist, his work says otherwise. A gallery in his Denver home is filled with mind-bending images, and it’s hard to imagine each started with a series of numbers and xs and ys that a computer interprets.
“I’m usually surprised at what I see once we put all those into the computer,” he says. “Sometimes, I don’t like it. But I’m always interested.”
Gudder got his artistic start in the 1960s, when his work required stacks of punch cards to enter a program that instructed a room-sized computer to move a stylus to create images. Today, he uses a large, commercial printer hooked to a home computer in his basement gallery. It’s been a lifelong passion, even leading him to pen a book on the topic in the 1970s.
Gudder’s first-year seminar class, Mathematical Art, shows students how mathematical instructions that start out as “Shadowplot 3D (Sin [x2] Cos [y2] , (x, -2, 2) …” create a strange, brightly colored image on a computer screen.
First-year communications major Jamie D’Angelo of Denver seems a quick study, manipulating Gudder’s equations on her computer screen, deftly creating new images by tweaking variables and substituting values into formulas.
“It’s not exactly what I had thought it would be,” D’Angelo says. “But I’m remembering a lot of math that I haven’t done in years, and that’s a good thing.”
Gudder, who offers the seminar to non-math majors, says the trick is to teach a math course without making it seem like a math course.
Gary Greenfield, a professor of computer science and mathematics at the University of Richmond, edits the Journal of Mathematics and the Arts. He says the combination of math and art is a complicated marriage viewed differently by artists. As he points out, some use mathematics to create art, and some find artistic inspiration in mathematics. It’s all about finding a creative outlet.
“Regardless of how you categorize it, or which kinds of art or artists are included,” Greenfield says, “in my opinion the reason the imagery exhibited often has such widespread public appeal—even though it is often disdained or ignored by the established art culture—is because we humans are instinctively drawn to order, symmetry, regularity, geometry, pattern, etc.”
“We see mathematics all around us, even in nature,” Gudder says. “Perhaps that’s why some of my art looks like it reflects a natural scene. You just have to look for it.”