What do fluid flows and Picasso drawings have in common? It turns out they both provide fertile ground for new applications of persistent homology. In this talk, we'll first show how persistent homology helps us to see the dynamics of simulated fuel combustion. We'll then discuss an application of persistence to analyzing the complicated patterns seen in convection flows. Finally, we'll wrap things up with a sneak peek at how persistence might be able to help solve a computer vision problem in the computational study of fine art.