Axelrod's agent based modeling-steps to convergenc

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Axelrod's model is a grid of agents who all have features that are randomly assigned. The probability they interact is determined by their similarity in traits. The grid will eventually converge and no interactions can take place because every agent will either be completely similar or dissimilar. I am wondering if you assume even distribution of the random features in the beginning if one could calculate an expected number of steps until convergence on a given grid size. Maybe using Markov chains?