  We study an autocatalytic reaction-diffusion scheme, the Gray-Scott model,
when the mixing processes do not homogenize the reactants. Starting from the
master equation, we derive the resulting coupled, nonlinear, stochastic partial
differential equations that rigorously include the spatio-temporal fluctuations
resulting from the interplay between the reaction and mixing processes. The
fields are complex and depend on correlated complex noise terms. We implement a
novel method to solve for these complex fields numerically and extract accurate
information about the system evolution and stationary states under different
mixing regimes. Through this example, we show how the reaction induced
fluctuations interact with the temporal nonlinearities leading to results that
differ significantly from the mean-field (perfectly mixed) approach. This
procedure can be applied to an arbitrary non-linear reaction diffusion scheme.
