Many who study complex systems believe that the complexity we observe in the world around us is frequently the product of a large number of interactions between components following a simple rule. However, the task of discerning the rule governing the evolution of any given system is often quite difficult, requiring intuition, guesswork, and a great deal of expertise in that domain. To circumvent this issue, researchers have considered the inverse problem where one searches among many candidate rules to reveal those producing interesting behavior. This approach has its own challenges because the search space grows exponentially and interesting behavior is rare and difficult to rigorously define. Therefore, the contribution of this work includes tools and techniques for searching for dimer automaton rules that exhibit self-organization (the transformation of disorder into structure in the absence of centralized control). Dimer automata are simple, discrete, asynchronous rewriting systems that operate over the edges of an arbitrary graph. Specifically, these contributions include a number of novel, surprising, and useful applications of dimer automata, practical methods for measuring self-organization, advanced techniques for searching for dimer automaton rules, and two efficient GPU parallelizations of dimer automata to make searching and simulation more tractable. / Ph. D.