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WIU Professor Transitions Fractal Art to App Technology

September 28, 2015

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MACOMB, IL – A Western Illinois University professor is taking the mathematical art of fractals to a new, technological level by developing a set of downloadable "apps," now available at the Apple App Store.

Mathematics Professor Fedor Andreev developed the apps with the help of Rutgers University Computer Science Professor Bahman Kalantari, the brother of WIU Department of Mathematics Chair Iraj Kalantari, who also made a significant contribution to the project. The trio worked on the software, designed to better control fractals.

"We set out to make some apps with fractal images with the ability to control the images; to use tools to change or adjust them," Andreev said. "The algorithms we ended up with allowed us to do that and more. Surprisingly, sometimes they produce images which are not technically fractals, in the narrow sense of the word, but are just as intricate and intriguing."

The result was the development of Poly-z-Vision, an app-designing collaboration that encourages mathematically-inspired image creation.

Fractals are designed using polynomial equations, the solutions that produce never-ending geometric shapes and patterns. They are created by repeating a simple process over and over in an ongoing feedback loop, resulting in "pictures of chaos," according to Andreev.

"Fractal patterns are probably familiar to most of us nowadays. They can be found in nature. Trees, rivers, coastlines, mountains, clouds, seashells, hurricanes - they all demonstrate fractal-like structures," said Andreev. "Abstract fractals can be generated by a computer calculating a simple equation over and over. But the only thing you should really know about fractals is that they are in the 'Frozen' song 'Let It Go. As the lyrics go, 'spiraling in frozen fractals all around,' you can see geometric precision and the beauty of a snowflake with infinite intricacy and symmetry."

Once the fractal-producing software was secured, Andreev tested it with middle school teachers and through students participating in Western's "Girls Plus Math" summer camp, for girls ages 11-13.

"The girls were given the early version of the app," Andreev said. "They experimented with it and then shared their experiences. We also showed the earlier versions to teachers so they can use the tools to inspire students in mathematics."

While polynomial equations and the concept of fractals could be intimidating, Andreev said the goal of the apps is to make it the mathematical concepts more understandable.

"A lot of people think, 'Wow, that is nice, but I would not be able to produce something like that ever," he said. "That is the typical reaction from many of my users. The whole idea of the app is to make it possible – a user, any user, can indeed produce those images. After experimentation, with tweaking and options, it is absolutely possible to produce intriguing images with the help of the Poly-z-Vision apps – no mathematical proficiency needed."

Through the Poly-z-Vision apps, users of iPads and iPhones can control the mathematically-generated images with just a swipe on the screen, using various moveable points to create unique designs. The apps also allow users to take photographs of their creations and save them on their devices.

Three versions of the apps are available, mostly based on the intended pattern of the images; one free to users, while the other two are 99-cents each to download.

"We aspire to keep the apps user-friendly and to encourage people to try it," Andreev said. "As a programmer, I understand the mathematics behind fractals, but I am aspiring to understand some of the art."

The initial app submission was accepted by the App Store over the summer, with the other two published in August.

The apps were submitted to the App Store to make them more available so "students of all ages and art enthusiasts" would have easier access to try them out, said Andreev. He and the Kalantari brothers continue to work on updates to make the apps easier to use. They are also working on bringing the apps to Android technology.

For more information about the apps, visit or cont
act Andreev at For more information about fractals, visit

Posted By: Jodi Pospeschil (
Office of University Communications & Marketing