A visualisation of the Douglas-Rachford Algorithm created by Scott Lindstrom, Jonathan M Borwein, Brailey Sims, Matthew P Skerritt, and Anna Schneider.
Here we see basins of periodicity for an iterative method applied to solving a perturbed version of the
phase retrieval problem. We run the Douglas-Rachford algorithm starting from each individual pixel in the
plane. We assign to each pixel a point, and then we color the pixel according to the behaviour of the point
under the dynamical system. Colours were inspired by Australian aboriginal artwork. The patterns which
emerge in this image are more polyhedral than one might expect. This picture is the main poster image for
Australian Mathematical Society special interest group Mathematics of Computation and Optimization (MoCaO).
It was featured at the Bridges Math Art conference in Stockholm, Sweden.