The polymerization of actin via branching at a cell membrane containing nucleation-promoting factors is simulated using a stochastic-growth methodology. The polymerized-actin distribution displays three types of behavior: (a) traveling waves, (b) moving patches, and (c) random fluctuations. Increasing actin concentration causes a transition from patches to waves. The waves and patches move by a treadmilling mechanism not involving myosin II. The effects of downregulation of key proteins on actin wave behavior are evaluated.