Spatial suppression of error catastrophe in a growing pattern

Error catastrophe is studied in a growing pattern with cellular automata. It is found that, although the critical error threshold P c for error catastrophe decreases monotonically with decreasing diffusion coefficient D, P c remains at a finite value in the limit that D goes to 0 because particles with higher growth rate repress the growth of those with lower growth rate spatially. The possibility that the spatial structure accelerates the evolution is also discussed.