A Franklin & Marshall College exchange student from Bolzano, Italy, has created a software application for Apple's iPhone that could revolutionize how students learn abstract math concepts.

Michael Dijori, a student from the Free University of Bolzano, last semester attended F&M, where he developed "Fractal Editor," a program where shapes and pictures can be created and used as an educational tool for those studying certain higher mathematical concepts such as linear algebra.

A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-sized copy of itself.

The application works by placing a few shapes on the phone's touchscreen with either a one- or two-finger tap and then resizing, moving, rotating and shearing the images.

Dijori developed the application under the supervision of Jay Anderson, an F&M computer science professor.

Earlier this month, Dijori, 20, learned that Apple Inc. accepted the application. It is now available to download for free from Apple's online iTunes store.

Dijori, who is now in his third semester at the Free University of Bolzano, said in an e-mail interview Tuesday that he was shocked that Apple accepted the application.

"Yes, I was really. Actually, I didn't plan to send the application to Apple. … Professor Anderson decided to do this, and I was really surprised," Dijori said.

Dijori, who worked on the independent study project for about 300 hours, was not paid by Apple for the application. However, he has found the fruits of his labor rewarding.

 "I am now happy to see a running application. I enjoyed working on that project because normally we computer science students write only applications for personal computers or Macintoshes," Dijori said. "Now, when I see an application written by me running on a mobile device, it is very satisfying. Also, many friends of mine have an iPhone and can run my application. The only negative point is that I don't have an iPhone, so I can't run my own application anymore."

Anderson established an exchange program with the Free University of Bolzano while on sabbatical at the school during the 2005-06 school year.

Anderson, who is once again studying at the Free University of Bolzano, said by phone Monday that Dijori is a fine student.

"I am absolutely thrilled … overjoyed," Anderson said. "Since we've gotten the news, there has been so much excitement in Bolzano. It makes me so proud."

Dijori's "Fractal Editor" application originally was rejected by Apple last fall, but Anderson advised Dijori to tweak the application and resubmit it.

As a basis for the application, Dijori redesigned a fractal program used for a PC or Macintosh by a former F&M student and made it compatible for an iPhone.

Dijori said parts of creating the application were difficult because designing a program for an iPhone is completely different from designing one for a computer.

"One thing is that I had to develop the project on my own, which also was new for me," Dijori said. "This means that I had to investigate developing applications on the iPhone. I had not a professor who taught me the programming language and the approach and so on. Scheduling also was important. I had no fixed times to work on it. So it was important that I work regularly on the project and that I finished it on time."

Anderson said it's amazing that a young student like Dijori was able to build such an intricate program.

"It's rare for a student to get so far so fast. I don't know if this is a flash in the pan because the concept is so new," Anderson said. "It will be interesting to see if hand-held applications will be useful in the area of higher education. But I bet a lot of people will use it to make pretty pictures."

E-mail: mpennino@lnpnews.com