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Cellular Automata : new constructions and dynamics

In this paper the dynamical behavior of two–dimensional cellular automata (2D CA) is studied. The notion of closingness is generalized to the 2D case and it is linked to permutivity and openness. The major contributions of this work are two deep constructions which have been fundamental in order to prove our new results. The authors strongly believe they will be a valuable tool for proving other new results in the near future.