Newton’s Method bursts out of the canvas of curves and colors in the McMillan gallery. The art seems to fold forever into itself, repeating the same bubbles. These amazingly intricate pieces were created by graduate student Cruz Godar. “I can’t remember not wanting to go into math,” Godar, the artist behind the Generative Art: The Beautiful Side of Math exhibit, said. Godar’s parents claim he was playing with pi at 3 years old.
At 11 years old, he started higher education at Cuesta College. Even after all that time, he still enjoys math. His passion is reflected in what he has created with his fractals and applets. Fractals are visual representations of equations beyond a traditional formula pattern that one might expect to see in a traditional math class. They can be created using individual methods or equations. The equations create curved shapes that are repeated through every inch of the piece, even down to what isn’t visible. These fractals can then be displayed on applets created by Godar to be more interactive and faster on the internet. Applets are computer based applications that allow Godar to create his visual art.
When looking at one of the fractals in the gallery, like Newton’s Method, the pattern seems finite. But, if you could zoom in the pattern of curves and points, it would keep going in an infinite pattern that goes on forever. “Fractals represent something that can’t exist and is infinitely complicated, yet our brains can still comprehend,” Godar said.
When Godar first started working with these applets, it wasn’t easy: “When you’re learning how to program, doing just basic logic is the first step. Actually getting an image is kind of a mess.” The programs he originally used would take all night to load one image.
“If you want to program and make the fractals look nice and do it on a large scale, it can be challenging,” associate math professor Ellen Eischen, who helped curate Godar’s art for the Creativity Counts gallery, said.
Godar found a spark to improve his fractal programs after he led a summer camp for advanced junior high school math students.
“I ended up having very large motivation to get this thing good and not be completely embarrassed by it taking five hours to do anything,” Godar said.
Wanting to share his work and wanting a place for his future work as a graduate student, Godar started his website. This proved fruitful because graphics on the web are more interactive, according to Godar. Many applets on his website show more of the complexities of math, while giving the user freedom to explore.
“Someone who knows nothing about any of this can go in and be like, ‘Look at the pretty pictures; I want to learn more,’” Godar said.
This website has been his hobby for the past three years. While looking through these applets, one could push the numbers and see how far they could go, thus learning more about these theorems. “The applets are the only interactive ones I’ve seen,” Godar said. All the hours of coding and testing Godar put into these applets, from the first trials with the Wilson’s Algorithm to the 3-D rendering of The Mandelbulb, all went into the creation of Wilson: a JavaScript collection to create applets.
Godar said, “The longest time wasn’t even spent getting this thing to work. It was just rendering a single sphere on a black void… just getting that to work was incredible.” Using the graphics processing unit on the computer opened the door to use it for the other fractals.
The use of color that makes these pieces pop, in the gallery and in applets, was added to draw the viewer in and expose the connections within the piece. “The color is pretty, but it also shows you a structure that is hidden,” Godar said. This makes it easier to make sense of the fractals than a black and white one. This drew me in and showed the beauty one might not see with just the numbers. Professor Eischen hopes the people who view the work will “see the aesthetic side of math and then get drawn in a bit because of these little blurbs next to each piece. Hopefully, it piques their curiosity.”
Godar will continue his work with fractals into the future. After the start of the gallery, many other professors have sent him ideas and other coding concepts to work on. Similar to a fractal, the next shape Godar’s work takes has infinite possibilities.
The exhibit runs in the Adell McMillan Gallery in the Erb Memorial Union through Oct. 29, with a closing reception on Oct. 28 at 6 p.m.
