We describe a three-species mechanism for spatial pattern formation in which only one species spatially moves. We show that a bifurca-tion to traveling or standing waves occurs. We contrast this mechanism for pattern formation with the better known cases where more than one species moves.

We have observed transverse pattern formation leading to highly regular structures in both the near and far fields when a near-resonant laser beam propagates without feedback through an atomic sodium vapor. One example is a regular far-field honeycomb pattern, which results from the transformation of the laser beam within the vapor into a stable three-lobed structure with a uniform phase distri...

Pattern formation in development is a complex process which involves spatially distributed signals called morphogens that influence gene expression and thus the phenotypic identity of cells. Usually different cell types are spatially segregated, and the boundary between them may be determined by a threshold value of some state variable. The question arises as to how sensitive the location of su...