Cellular automaton model of self-healing

We propose a simple cellular automaton model of a self-healing system and investigate its properties. In the model, the substrate is a two-dimensionalcheckerboardconfigurationwhichcanbedamagedbychangingvaluesofafinitenumberofsites.Thecellularautomatonweconsiderisacheckerboardvoting rule, a binary rule with Moore neighborhood which is topologically conjugate to the majority voting rule. For a single-color damage (when only cells in the same state are modified), the rule always fixes the damage. For a general damage, when it is localized inside a 3x3 square, the rule also fixesit always. When the damage is inside of a largernxnsquare, the efficiency of the rule in fixing the damage becomes smaller than 100%, but it remains better than 98% forn <= 5 and better than 75% for n <= 7. We show that in the limit of infiniten the efficiency tends to zero