Automata networks are often conceived as a finite generalization of cellular automata. In this paper, we prove that the limit dynamics of any finite automata network under the parallel update schedule correspond exactly to the fixed points of so-called strictly one-way cellular automata. This correspondence is proven to be exact, as any strictly one-way cellular automata can be transformed into a corresponding automata network, where the attractors of the latter correspond exactly to the fixed points of the former. This transformation is easy to operate by using output functions which have been developed in the author's previous works.