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The Kauffman model of genetic computation highlights the importance ofcriticality at the border of order and chaos. But our understanding of itsbehavior is incomplete, and much of what we do know relies on heuristicarguments. To better understand the model and obtain more rigorous insights, weshow that there are fundamental links between the critical Kauffman model andaspects of number theory. Using these connections, we prove that the number ofattractors and the mean attractor length grow faster than previously believed.Our work suggests that techniques from number theory, which are less familiarto the physics community, may be the right tools for fully cracking theKauffman model.

Insights from number theory into the critical Kauffman model with connectivity one