Small GTPases from the Rho family represent a group of signaling proteins responsible for the regulation and coordination of numerous cellular activities guided by the actin cytoskeleton. Among eukaryotic cells, Dictyostelium discoideum amoebas are capable of the fastest reorganization of the actin network, and can reverse their polarity within one minute. As such, they represent a basic testing ground for conceptual models linking small GTPases and their signaling pathways to cell morphodynamics during migration. In D. discoideum, active Rac1 regulates actin polymerases at the leading edge and actin filament-bundling proteins at the trailing end of polarized cells. We monitored the spatio-temporal distribution of Rac1 activity using a specific fluorescent probe, and in addition to irregular patterns, we also observed the appearance of regular patterns, in the form of stable polarization, as well as traveling and standing waves. We conducted a systematic analysis of mean field reaction-diffusion models with reactions that follow the law of mass action, and identified a minimal model that can reproduce the observed regular patterns. We used a variant of this model to describe the dynamics of Rac1 GTPase and its effector protein DGAP1. Besides successfully reproducing individual features of the experimentally observed dynamic patterns of fluorescently labeled proteins, the model also reproduced the predominantly negative spatio-temporal correlation between Rac1 and DGAP1. In addition to the mean field model, we developed a stochastic model in order to analyze the impact of random fluctuations on the behavior of the system, and established their key role in spontaneous transitions between different types of protein patterns.