Periodic wave patterns are widely observed in oscillatory or excitable chemical systems and in multicellular systems. More recently, waves of cortical activity, linked to actin dynamics in many cases, have been documented in a variety of single-cell systems, including various immune cell types. I will discuss our understanding of the pattern formation mechanisms on the cortical region of mast cells, including the molecular definitions underlying a number of wave characteristics. These spatial and temporal patterns represent attractor states in dynamical systems, which describe the trajectory a system gravitates towards depending on the network topology, control parameter, and sometimes initial conditions. We are particularly interested in applying this dynamical framework to understand lipid metabolism, actin dynamics and signal transduction that controls fundamental cell biological processes such as mitosis.