The time dependence of the fluorescence anisotropy expected when a fluorophore exists in distinct environments having different fluorescence decay and motional behavior is illustrated by simulation calculations. A wide range of behavior is observed. The analysis of such decays in terms of the underlying physical parameters is also illustrated and discussed. In particular, the analysis of 'associated' heterogeneous behavior using a homogeneous environment model with complex motional behavior is evaluated. It is argued that anisotropy decays that exhibit a high initial anisotropy and that rise at long times must be due to a heterogeneous environment. Anisotropic rotor diffusion cannot give rise to behavior of this type. A similar conclusion is reached for anisotropies that exhibit downward curvature. On the other hand, anisotropy decays that are monotonically decreasing and have a positive second derivative at all times cannot be analyzed in a unique fashion and therefore an ambiguity exists in the interpretation of such data in terms of motional behavior.