In this paper we propose the two methods to reproduce given binary pattern dynamics with cellular automata. The point is that one can easily find a sequence of rules or specified rules in two-state multineighbors cellular automata, which enable an errorless description and reproduction of given multiple sequences of binary patterns. Actual examples using computer experiments for one-dimensional bit-pattern data (digital sound signals, multiple sequences of cycle patterns) are given. Noise robustness and the other important dynamical properties of these methods are investigated from the perspective of "rule dynamics" and in comparison with a recurrent neural network model, which enables us to embed given binary patterns as multiple attractors in the form of fixed points or limit cycles.