A mosaic of barren grounds (bars) and areas covered by vegetation often forms in grassy or shrubby communities in conditions of scarcity of environmental resources (e.g., water). Such landscapes have been named “two-phase mosaics”; this term emphasizes the discreteness of vegetation cover units. Fairy rings (FRs) are an example of such structures. There are two sets of competing hypotheses on the reasons behind FR formation: insect activity and self-organization. One of the main arguments against the second set of hypotheses is their inability to explain the FR life cycle: their emergence, ripening, maturation, and disappearance (death). The article proposes a simple cellular-automaton model of the vegetation cover formation. The model imitates the scarcity of resources (water and ash constituents) and generates different variants of the two-phase mosaic. The results depend on two parameters: limitation of resource inflow and plant growth rate. Sixteen percent of combinations of these parameters result in the formation of structures similar to FRs. The model reproduces not only the vegetation distribution pattern observed in the nature but also individual FR life cycles that are consistent with field descriptions. Thus, the model removes the main objection to self-organization as the main mechanism of FR formation.