  We study the properties of the ``Rigid Laplacian'' operator, that is we
consider solutions of the Laplacian equation in the presence of fixed
truncation errors. The dynamics of convergence to the correct analytical
solution displays the presence of a metastable set of numerical solutions,
whose presence can be related to granularity. We provide some scaling analysis
in order to determine the value of the exponents characterizing the process. We
believe that this prototype model is also suitable to provide an explanation of
the widespread presence of power-law in social and economic system where
information and decision diffuse, with errors and delay from agent to agent.
