Matthew P. Skerritt
I am a Mathematics PhD student at the University of Newcastle, Australia. I have, on occasion, found cause to use visualisation techniques to give mathematical insight into research I have been involved in. My preferred method of visualisation is to write GPU software to compute high resolution images related to the research at hand. The images I have produced tend to be intricate and visually appealing. I have found that these images are greatly enhanced when printed at high resolution in large format.
As part of research into the Douglas–Rachford algorithm applied to an eclipse and line we wished to visualise the basins of attraction. I wrote GPU software to compute these basins quickly at high resolution. The resultant images provided hitherto unavailable insight (see “Dynamics of the Douglas-Rachford Method for Ellipses and p-Spheres” in Set-Valued and Variational Analysis 2017).
The dimensions for this work have been chosen to show small scale detail, large scale behaviour, and some unexpected properties. The colour scheme used differs to that found in the research paper. It was chosen to enhance the aesthetic appeal of the image—although at the expense of mathematical clarity—and is based on Australian aboriginal artwork.