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The Kauffman model is a simple model of genetic computation which highlights the importance of critical behavior at the border of order and chaos. We present a simple proof that the number and length of attractors for the critical Kauffman model with connectivity one exhibit super-polynomial growth with the size of the network, improving on the best known bounds. Our approach is to bound the mean attractor length from above and below using elementary methods in number theory.
Submitted (2023)