Abstract
A Markov chain model is constructed to simulate pattern formation arising from an evolutionary population of interactive homogeneous agents. In the structure of optimal evolution and stochastic properties, the model exhibits emergent properties with rich dynamical diagrams. We study the cluster splitting transition with the coarsening period-adding phenomena shown by the model, which gives an example of pattern formation in the evolution of complex system and reveals dynamical behavior of the Markov chain process.
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