Math + computer science = coloring book for Barnes, Kreahling

WCU’s Bill Kreahling (left) and Julie Barnes are co-authors of “Coloring Book of Complex Function Representations,” which has become popular on the math circuit.

Western Carolina University professor of mathematics Julie Barnes was working with Beth Schaubroeck, a professor of mathematics at the Air Force Academy, on a research project related to complex numbers when the two noticed their work was generating some interesting images.

As they continued writing their math, Barnes noticed that the images resembled those found in adult coloring books. So, they decided to put together a complex function coloring book as holiday presents for friends and family.

The book was a hit among their mathematician and non-mathematician friends and family – even neighbors wanted copies. While attending a Mathematical Association of America meeting, Barnes met with senior book acquisitions editor Stephen Kennedy about publishing a book on hands-on teaching ideas. She also mentioned the coloring book.

Kennedy was intrigued with the coloring book, but suggested coming up with more interesting images, and describing the math that produced the image. That required the use of Julia sets, which are sets of complex numbers that are visualized by plotting in the complex plane.

“Once we realized the math behind it, we were able to get more interesting images,” Barnes said. “To describe the math, it’s related to Julia sets. We couldn’t do that without Julia sets, so we went to the computer scientist and got him to generate some.

Enter Bill Kreahling, WCU associate professor of computer science. “For the explanation of where these pictures came from, they needed images of the Julia sets which they’re based on,” Kreahling said. “While there are other programs out there that create them, if you go to a website, you’re not going to get high resolution images, or if you do, they’re going to be copyrighted by whoever did it. I wrote a program that would generate Julia set images at whatever resolution they needed.”

Those images, and the math behind it, turned into the “Coloring Book of Complex Function Representations.” The book was initially sold last summer at the Mathematics Association of America meetings.

“They’d never seen books go that fast,” Barnes said. “There were people lined up and they started buying like 10 copies. There was a huge quantity going.”

The 39-page book features 18 images and the math that produced them. The majority of the royalties from the book sales go the MAA’s Project Next, a national professional development program for those who recently completed their doctorates in mathematical sciences.

For more information on how to purchase the coloring book, contact Barnes at 828-227-3943 or