Cellular automaton model of self-healing

Abstract

We propose a simple cellular automaton model of a self-healing system and investigate its properties. In the model, the substrate is a two-dimensional checkerboard configuration which can be damaged by changing values of a finite number of sites. The cellular automaton we consider is a checkerboard voting 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 3 × 3 square, the rule also fixes it always. When the damage is inside of a larger n × n square, the efficiency of the rule in fixing the damage becomes smaller than 100 % , but it remains better than 98 % for n ≤ 5 and better than 75 % for n ≤ 7 . We show that in the limit of infinite n the efficiency tends to zero.