This paper presents a readily accessible patterning platform--based upon geometric constraints, discrete cell suspension droplets, and controlled cell settling--that provides both temporal and spatial patterning capabilities. As a demonstration, single-cell (and bead) suspensions as well as multicellular human embryonic stem cell colonies are spatiotemporally patterned onto arbitrary substrates. These substrates include tissue culture surfaces, cell monolayers, protein-coated surfaces, and 3D gel matrices. The generation of soluble factor gradients is also demonstrated. This method is completely passive and does not require external power sources. Spatiotemporal patterning provides a foundation for future biological studies that explore the time-dependent relationships between cell-cell signaling and cellular responses.