Mixing of granular materials provides fascinating examples of pattern forma
tion and self-organization. More mixing action - for example, increasing th
e forcing with more vigorous shaking or faster tumbling - does not guarante
e a better-mixed final system. This is because granular mixtures of just ba
rely different materials segregate according to density and size; in fact,
the very same forcing used to mix may unmix. Self-organization results from
two competing effects: chaotic advection or chaotic mixing, as in the case
of fluids, and flow-induced segregation, a phenomenon without parallel in
fluids. The rich array of behaviors is ideally suited for nonlinear-dynamic
s-based inspection. Moreover, the interplay with experiments is immediate.
In fact, these systems may constitute the simplest example of coexistence b
etween chaos and self-organization that can be studied in the laboratory. W
e present a concise summary of the necessary theoretical background and cen
tral physical ideas accompanied by illustrative experimental results to aid
the reader in exploring this fascinating new area.