For critical K=1 Boolean networks, attractor lengths are governed by the order of the permutation induced by feedback loops, yielding typical maximum lengths exp[(1/2)ln^2 N], extremal lengths exp[sqrt(N ln N)], and mean length exp[N^(1/3)].
Boolean modeling in systems biology: an overview of methodology and applications.Physical biology, 9(5):055001, 2012
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Permutation theory governs long-term dynamics of critical Boolean networks
For critical K=1 Boolean networks, attractor lengths are governed by the order of the permutation induced by feedback loops, yielding typical maximum lengths exp[(1/2)ln^2 N], extremal lengths exp[sqrt(N ln N)], and mean length exp[N^(1/3)].