  We describe a new algorithm for simulating complex Markoff-processes. We have
used a reaction-cell method in order to simulate arbitrary reactions. It can be
used for any kind of RDS on arbitrary topologies, including fractal dimensions
or configurations not being related to any spatial geometry. The events within
a single cell are managed by an event handler which has been implemented
independently of the system studied. The method is exact on the Markoff level
including the correct treatment of finite numbers of molecules. To demonstrate
its properties, we apply it on a very simple reaction-diffusion-systems (RDS).
The chemical equations A+A -> inert and A+B -> inert in 1 to 4 dimensions serve
as models for systems whose dynamics on an intermediate time scale are governed
by fluctuations. We compare our results to the analytic approach by the scaling
ansatz. The simulations confirm the exponents of the A+B system within
statistical errors, including the logarithmic corrections in the dimension d=2.
The method is capable to simulate the crossover from the reaction to diffusion
limited regime, which is defined by a crossover time depending on the system
size.
