Centre College Assistant Professor of Physics James Kelly’s first-year CentreTerm course, “Chaos and Fractals: A Revolution in Science,” helped students understand how extremely complicated behavior arises in the motion of very simple dynamic systems while exploring the beauty of those chaotic systems. Even more interestingly, students were able to create visual representations of the closely-associated intricate structures, known as fractals, using a 3D printer.
Kelly says that, although this is the fourth time he’s taught the course, adding the technology of 3D printing brought a whole new dimension.
“I have always wanted the students to be able to design and produce 3D fractals, but we didn’t have a 3D printer at the time,” Kelly says. “In the past I would encourage students to build models as part of a final project, but I would only have one or two takers because it’s a lot of labor to create a 3D fractal by hand, and weight and strength become an issue when they get very large.
“I have a poster of a fractal called the Mandelbrot set on the wall of my office that I computed and printed myself one screen shot at a time on a dot matrix printer back in the 80s,” he continues. “Things have gotten a lot faster and more sophisticated since then, first with graphics on the screen, then with 2D laser printing, and now with 3D printing. It is a great topic for a first-year course, because the natural beauty of fractals pulls you in right from the start.”
But for at least one student, Kelly’s class wasn’t exactly love at first sight.
“I believe my experience was different from most for the very fact that I was one of the only students that had a very small — emphasis on ‘small’ — interest in mathematics, or physics for that matter,” says Nicolaus Stengl ’18. “Going into the class, I believed I was going to major in philosophy and English, so the first week I disliked the course.
“I went to talk with Dr. Kelly and we discussed what I was having trouble with, and I subsequently ended up going to his office every morning for the second week receiving his assistance,” Stengl explains. “Slowly but surely I began to enjoy it, and my most important learning experience was the connection between philosophy and physics. Now I plan not only to major in philosophy but also physics. I never thought I would do such a thing, but this course did something to me.”
As a motivational tool, Kelly required the students to photograph their 3D printed fractals and post them on thingiverse.com, the leading online repository for 3D-printable files.
“Molly Holder ’18 was one of the first to design, print and post her design, and she got a lot of immediate positive feedback, along with a request for a short story about her design on 3Dprint.com,” Kelly says. “I think she was really surprised by the attention and interest in her design, as we all were.”
As a result of the class, Holder says she’s even more interested in mathematics and also interested in physics and computer science. “Chaos and fractals concepts were completely new to me, but now I find them so interesting.”
Will Hellman ’18 agrees. “Nature itself is extremely complicated and even chaotic at times, but there are underlying equations and formulas which govern the behavior of everything,” he says. “We can then model those equations on computers and get results like fractals and other chaotic forms which are really fun to look at.
“It’s pretty awesome to walk around campus now, because I see fractals everywhere. The trees are fractals, the clouds are fractals, and almost everything else seems to have some kind of fractal in it,” he continues. “The class really changed the way I look at things, and I recommend it to anyone who likes to learn a lot about how the world works.”
Read the entire interview with Molly Holder for 3Dprint.com.
Above: 3D printed fractal by Molly Holder ’18
by Cindy Long