  Dissipative structures are generally observed when a system relaxes from a
far from equilibrium state. To address the reverse question given by the title,
we investigate the relaxation process in a closed chemical reaction-diffusion
system which can potentially form Turing-like patterns during the transient. We
find that when certain conditions are fulfilled the relaxation process is
indeed drastically hindered, once the pattern is formed. This slowing-down is
shown to be due to stepwise relaxation, where each plateau in the relaxation
process corresponds to residence at a certain spatial pattern. Universality of
the phenomena as well as their biological relevance is briefly discussed.
