  We study the effect of fractal initial conditions in closed reactive systems
in the cases of both mobile and immobile reactants. For the reaction $A+A\to
A$, in the absence of diffusion, the mean number of particles $A$ is shown to
decay exponentially to a steady state which depends on the details of the
initial conditions. The nature of this dependence is demonstrated both
analytically and numerically. In contrast, when diffusion is incorporated, it
is shown that the mean number of particles $<N(t)>$ decays asymptotically as
$t^{-d_f/2}$, the memory of the initial conditions being now carried by the
dynamical power law exponent. The latter is fully determined by the fractal
dimension $d_f$ of the initial conditions.
