The cell cycle is a tightly controlled process, yet it shows marked differences across species. Which of its structural features follow solely from the ability to control gene expression? We tackle this question in silico by examining the ensemble of all regulatory networks which satisfy the constraint of producing a given sequence of gene expressions. We focus on three cell cycle profiles coming from baker's yeast, fission yeast, and mammals. First, we show that the networks in each of the ensembles use just a few interactions that are repeatedly reused as building blocks. Second, we find an enrichment in network motifs that is similar in the two yeast cell cycle systems investigated. These motifs do not have autonomous functions, yet they reveal a regulatory logic for cell cycling based on a feed-forward cascade of activating interactions.