Space & Innovation

Math Artist Finds the Beauty in Equations: Photos

An Iranian mathematics student generates beautiful images using custom-coded computer techniques.

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Don't try to tell my seventh grader this, but the truth is that math is beautiful. That's the thesis sentiment behind the work of Iranian artist Hamid Naderi Yeganeh, who uses his own custom-coded computer programs to transform mathematical equations into gorgeous works of line art. Yeganeh, a 25-year-old mathematics student at the University of Qom in Iran, has generated thousands of images using his unique computational techniques. He recently sent a batch to DNews along with some thoughts on his process -- let's take a look.

“I started to create mathematical images by computer programs in 2012,” Yeganeh says in an email to DNews. “At first, I was interested to make beautiful images by using basic mathematical concepts such as line segments, circles, trigonometric functions, etc.”

Yeganeh uses different methods to produce images. His first program, which he still uses today, is designed to output thousands of images generated by specific equations employing a series of variables. Yeganeh culls through the output images to find interesting designs.

“After a while, I understood that I can find some interesting mathematical shapes that resemble real things such as animals or sailboats,” Yeganeh says. “In order to find such shapes, I tried to test many formulas by computer programs.”

Yeganeh later developed a technique that offers a little more control, at the cost of a good deal more work on the mathematics end. He chooses a specific image -- a butterfly, say -- then tries to work out which formula will produce the desired picture.

Or, for instance, when Yeganeh wanted to generate some images of leaves and branches, he came up with a series of potential equations that eventually yielded several different kinds of pictures. Here we see his image titled, simply, Palm Branch.

The captions for Yeganeh's images can be an adventure, if you speak math. For “Olive Branch,” another in the series, the caption reads: “This image shows 4,000 circles. For k=1,2,3,...,4000 the center of the k-th circle is (X(k), Y(k)) and the radius of the k-th circle is R(k), where X(k)=(2k/4000)+(1/28)sin(42πk/4000)+(1/9)(sin(21πk/4000))8+(1/4)(sin(21πk/4000))6sin((2π/5)(k/4000)12), Y(k)=(1/4)(k/4000)2+(1/4)((sin(21πk/4000))5+(1/28)sin(42πk/4000))cos((π/2)(k/4000)12), R(k)=(1/170)+(1/67)(sin(42πk/4000))2(1-(cos(21πk/4000))4).”

In honor of Pi Day -- March 14 (3.14) -- Yeganeh created this image of everyone's favorite mathematical constant, created from 2,000 circles. “Pi is an international number,” Yeganeh writes in his

blog series

. “This number can be a symbol of peace between nations.”

Yeganeh sometimes likes to set up particular challenges for himself. Since the human face has historically been a traditional subject for art, he created the image above using 12,000 circles.

Part of a series of images inspired by the continents, this tessellation image is created with a Northern America-like pentadecagon (15-sided polygon) and a South America-like pentagon. “Also, the complex number (1/2)^(1/8)*e^(2πi/8) plays an important role in this tessellation,” Yeganeh adds. Yeah, I was just gonna say. You can see more of Yeganeh's math-inspired art on his

gloriously sprawling website

. Now if I can just get him to start e-mailing with my seventh grader.