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Patterns are quotidian in nature. Distinct multiscale patterns are generallya consequence of nonequilibrium dynamical processes associated with mechanicalor hydrodynamic instabilities. In this thesis, I report experimentalinvestigations on pattern formation in a few examples of fluid and granularsystems, and uncover the underlying mechanisms that give rise to thosepatterns.  Leidenfrost drops are known to experience star-shaped oscillations withlittle damping. However, the underlying mechanism remains unclear. Here Ireport that the hydrodynamic coupling between the rapid evaporated vapor flowand vapor-liquid interface excites the star-shaped oscillations, suggesting apurely hydrodynamic origin.  Polygonal desiccation crack patterns are commonly observed in naturalsystems. However, it is unclear whether similar crack patterns spanningmultiple length scales share the same underlying physics. I report experimentalresults on polygonal cracks in drying suspensions of micron-sized particles. Incornstarch-water mixtures, multi-scale crack patterns were observed due to twodistinct desiccation mechanisms. We also find the characteristic area of thepolygonal cracks, and film thickness obey a universal power law.  Finally, I report sedimentations of non-Brownian particles in viscous fluids.We observed an effective repulsion between particles with nonuniform density inboth two-body and many-body systems in two and three dimensions, in contrast toparticles with uniform density. We also characterize the statistical propertiesof the sedimentation patterns of particles in three dimensions.  The patterns I report in this thesis represent typical examples in fluid andgranular systems that are driven by nonequilibrium dynamics, and the underlyingmechanisms we uncover are expected to enhance our understanding of how theseseemingly simple patterns arise in natural systems.

Experimental investigations on the nonequilibrium dynamics of pattern formation in fluid and granular systems