Abstract
The paper considers a class of elementary cellular automata such that any automaton of this class is equivalent to itself under the conjugation transformation or it is equivalent to itself under the combination of the conjugation and reflection transformations. We have studied cycles in the state space of each automaton and the rate of state transitions. We use the concept of the complementary automaton. We have proved that, if, for an automaton belonging to the studied class, the spectrum of average velocities contains a value <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$v_{0}$</tex> , then the spectrum of the complementary automaton contains also the value <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1-v_{0}$</tex> . The considered class contains 24 automata, and 10 of these automata can be interpreted as transport models. Morover, there are 4 cellular automata that are not belong to the considered class but may also be interpreted as traffic models.
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