Using ipad snaps to illustrate complex mathematics
What do blood vessels, ferns and crystals have in common? They are all examples of the beauty of fractals. Fractals are relative newcomers to the world of geometry, named by Benoit Mandelbrot in the mid-seventies. These complex, self-similar images can be described in terms of smaller copies of themselves.
This repetitive quality has long piqued the interest of mathematician Michael Barnsley. Working with a team including his wife Louisa, the researchers have developed a new way for everyone to see the beauty in the environment around them - through their fractal-based FrangoCamera ipad app.
“A fern leaf is a good example of a fractal,” says Barnsley. “As you look at the fern on a smaller and smaller scale, the pieces repeat each other. The frond is made of smaller branch-like pieces, which are made up of leaves – all repeating the same pattern, just on different scales.”
MSI is recognised by many as the ‘home’ of fractal geometry, after researcher John Hutchinson published the seminal paper Fractals and Self Similarity in 1981.
“The story of the FrangoCamera started abroad, at an art show in Florida,” he says. “Louisa, Dave Wilson and I were discussing the idea that fractal transformations could be done on the iPad. When we got back to Canberra, we formed Frango Studios, enlisting the help of Neville Smythe and Brendan Harding.”
The team spent the next fifteen months developing the application, which allows users to morph saved and real time images via the iPad camera, according to underlying fractal equations.
“Frango means ‘I broke’ in Italian, but the image isn’t being broken as such,” he explains. “The app is dismantling the image and reassembling it differently according to the underlying fractal rules contained within the sixteen different lenses.”
Barnsley says the application “steals the colours and pictures from the real world” transforming them into mesmerising images that hint at the subject matter, encouraging the user to see the world from another perspective. But this app is more than just a creative outlet. Barnsley is using it as an educational tool in his Fractal Geometry and Chaotic Dynamics class, helping students to visualise the maths. He hopes the app will bring his love of fractals to the masses.
“The app has an educational mission. We have included easily understood information explaining fractals, to help users understand what is happening to the image and to help them appreciate the underlying mathematics.”
Barnsley and his wife Louisa are both passionate environmentalists and seeing the world from another perspective is the real driver behind the project. Beyond the educational and creative mission, Michael says he wants “people to take the iPad out into nature, to help them see things for the first time again - to recognise the beauty within nature. Children are aware of this beauty in the world, and I wanted to help people see it again.”