UVic student completes solution of Mandelbrot’s problem

Eric Foxall

Benoit Mandelbrot is arguably one of the most well known mathematicians of modern times for his discovery of what we now call the Mandelbrot set, and for “fractals,” whose beautiful images have become the hallmark of the modern mathematical fields of dynamics and chaos. Mandelbrot also did seminal work in the analysis on the problem of ‘scaling’ in language and other fields. In 1955, he published a partial solution to this problem, but it remained incomplete until very recently.

Ten years ago, Rod Edwards, now Chair of the Department of Mathematics and Statistics, along with two colleagues from McGill—Ted Perkins and Leon Glass, started working on Mandelbrot’s incompletely solved problem as a side project.

Enter Eric Foxall, a graduate student in mathematics at UVic. Rod discussed the problem with Eric and asked if he could help. Eric more than helped. He produced the key piece of analysis that allowed the team to complete the solution. Not only that, Eric took it a step further and solved a more general problem than Rod and his colleagues had been aiming for. The technical result was published in the Electronic Journal of Linear Algebra, but the team has also shown, in a recent paper in Nature Communications (14 Oct. 2014), its wide applications in many fields ranging from protein folding to musical sequences.

Read the complete article in Science Matters Spring 2015