Convective magma mixing is driven by thermal and compositional effects on melt density. We investigated the role of compositional buoyancy in convective magma mixing by means of two-dimensional numerical simulation. Two kinds of self-organization phenomena were observed in our simulations: (1) temporally-local unmixing events associated with flow reversals; and (2) long-lived segregations (ocular structures) in the center of convection cells. Statistical quantities of scale, scale ratio, and intensity of segregation are useful abstractions of the composition field for quantifying mixing and self-organization phenomena. The trajectory of scale ratio and intensity exhibits attractor behavior and provides a compact way of monitoring the evolution of mixing and self-organization. The ratio of compositional buoyancy to thermal buoyancy is given by the parameter Rr, where Rr = 0 implies passive mixing and Rr > 0 implies dynamic mixing. Ocular structures which form in both passive and dynamic mixing tend to decrease the mixing rate. Flow reversals and associated unmixing events which occur only in dynamic mixing further slow mixing. However, passive mixing is slower in our simulations than is mixing with small Rr because a strong and persistent ocular structure forms in passive mixing. At high Rr (Rr > 1), however, mixing is generally inhibited by compositional buoyancy because of the gravitational stability of the initial state.