In this talk, we introduce the bifurcation tracing problem in reaction-diffusion problems and propose a framework for quantifying patterns using computational geometry tools such as alpha-shapes. Based on the pattern statistics, the Wasserstein distance is employed to trace transitions via predictor-corrector continuation. The method is demonstrated on reaction-diffusion systems, agent-based models, and fluid simulations. This talk is based on joint work with Bjorn Sandstede (Brown) and Sam Maffa (Broad Institute).