Recent experimental and computational studies show that ''islands'' (unmixed regions that do not interact with surrounding regions) are ubiquitous features in chaotically advecting fluids. Such islands quite naturally account for the geochemically inferred coexistence of apparently distinct, long-lived geochemical heterogeneity with relatively homogeneous regions of an actively convecting mantle. These results also indicate that mixing patterns-the set of islands and folds characterizing the large-scale material advection-are sensitive to small variation in the rheology of the fluid. Therefore, interpretation of numerical simulations of mantle transport and mixing is less straightforward than currently supposed. Computational studies of analytic flow solutions with systematically introduced and controlled errors indicate that mantle simulations are unlikely to accurately compute individual trajectories for even moderate time, but that trajectory ensembles can be accurately computed for long time. Significantly, computations also indicate that mixing and transport results may not evolve smoothly with increased rheological realism. ¿ American Geophysical Union 1995