A stochastic activity-transfer model, previously proposed to apply to turbulence, is studied and simulated on a 256 x 256 lattice. Introduction of random selfactivation does not allow stable fronts to develop in the limit of small growth probability. By assigning discrete density values equal to the threshold values in a related continuous and deterministic model, the structure functions for distances r in the lattice are calculated. They have a functional form different from the power behavior which in the case of the deterministic version was interpreted as another sign of self-organized criticality. Future studies of these and other models may be facilitated by the algorithm developed for structure function calculations.