Abstract
The dynamics of cellular automata that are homogeneous and symmetric with respect to up-down symmetry is expressed by the probability of the appearance of different neighbourhoods on a lattice. The distribution function found in computer simulations is used to specify the differences in the set of cellular automata. The intrinsic structure of a rule has been proposed to explain the results obtained. The problem of whether or not automata are stable, the length of time needed to reach the stabilization and the type of stabilization, are also discussed.
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