Landau meets Kauffman

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

A Kauffman network is a model of genetic computation that highlights the role of criticality at the border of order and chaos. But our limited theoretical understanding of it relies on convoluted arguments. We give a simple proof that the number of attractors for the critical model with connectivity one grows faster than previously believed. Our approach exploits a link between the critical dynamics and number theory.