Over The course of the last four years I have researched the consensus problem. I have done so by studying how cellular automata following the 2DGKL rule are able to reach consensus in a verity of ways. There are only certain structures that can form within a network, and these structures can be described and examined directly from the rules that make them up. I have also explored a variety of methods to study the rule including, graph theory and liner algebra representations of the cellular automata. Additionally I collected an analyzed data on symmetry in the rule, dependency on size and boundary conditions. I also have studied alternative rules.
Griffin, David, "The Consensus Problem, Cellular Automata, and Self-Replicating Structures" (2016). Physics Capstone Projects. Paper 35.