Gallery: Douglas-Rachford Algorithm

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.

Other visualisations by Scott Lindstrom can be found on his web page.