Persistence diagrams are extremely useful for describing complicated patterns in a simple but meaningful way. We will demonstrate this idea on the patterns appearing in the convection flows and granular media. This procedure allows us to transform samples from the experiment into a point cloud in the space of persistence diagrams. The space of persistence diagrams is a complete metric space. There is a whole family of matrices on this space. By choosing different metrics one can interrogate the pattern locally or globally which provides deeper insight into the dynamic of the process of pattern formation. The Morse-Conley database can be used to identify invariant sets of the dynamical system. We will concentrate on fixed points and periodic orbits.