The emergence, growth and stabilization of stationary concentration pa
tterns in a continuously fed chemical reaction-diffusion system are st
udied through numerical simulation of the Lengyel-Epstein model. This
model represents a key to understanding the recently obtained Turing s
tructures in the chlorite-iodide-malonic acid system. Using the supply
of iodine as a control parameter, the regularity of the hexagonal pat
terns that develop from the noise inflicted homogeneous steady state i
s examined. In the region where they are both stable, the competition
between Hopf oscillations and Turing stripes is studied by following t
he propagation of a front connecting the two modes. Finally, examples
are given for the types of structures that can develop when a gradient
in feed concentration is applied to the system.