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 use of projection algorithms for the computation of points of intersection of plane curves we examined two variants of the Douglas–Rachford algorithm. The first variant used Euclidean reflection, and the second variant used Schwarzian reflection (see “Computing intersections of implicitly specified plane curves” in the Journal of Nonlinear and Convex Analysis, Vol 18, No 3). In order to see the relative performance of each of these two variants I wrote GPU software to compute a high resolution grid of points coloured according to which variant performed better when beginning at that point: white for Schwarzian and black for Euclidean. The image revealed a rich and interesting pattern.