LAUSR

Pattern formation and selection are fundamental, omnipresent principles in nature—from small cells up to geological scales. InE. coli bacteria, for example, self-organized pole-to-pole oscillations ofMin proteins—resembling a short standingwave—ensure correct positioning of the cell division site. The same biochemical reaction leads to traveling proteinwaves on extendedmembranes in in vitro experiments. Are these seemingly contradictory observations of system-spanning importance?We show that a transition of nonlinear travelingwave patterns to reflection-induced standingwaves in short systems is a generic and robust phenomenon. It results from a competition between two basic phenomena in pattern formation theory.We confirm the genericfindings for the cell-biologicalMin reaction and for a chemical reaction–diffusion system. These standingwaves showbistability and adapt to varying system lengths similar as pole-to-pole oscillations in growing E. coli.Our generic results highlight key functions of universal principles for pattern formation in nature.