  We examine numerically different zero-dimensional reaction-diffusion
processes as candidate toy models for high-energy QCD evolution. Of the models
examined -- Reggeon Field Theory, Directed Percolation and Reversible Processes
-- only the latter shows the behaviour commonly expected, namely an increase of
the scattering amplitude with increasing rapidity. Further, we find that
increasing recombination terms, quantum loops and the heuristic inclusion of a
running of the couplings, generically slow down the evolution.
