Fig. 9. Control kernels in random networks show similar characteristics to those seen in the biological cases.

Here we choose networks of size 10, 15, and 20 from three ensembles: Erdös–Rényi networks with zero thresholds (azure triangles), Erdös–Rényi networks with balanced threshold inputs (dark purple circles), and p–K networks with random truth tables (pink diamonds). A Mean control kernel sizes are typically near the base-2 logarithm of the number of attractors. Compare to Fig. 1. Outliers, highlighted with a black circle, share a bias toward excitation that creates repellor fixed points. B The first-order approximation to control kernel size is typically below ${\log }_{2}r$ and always below $2{\log }_{2}r$. Compare to Fig. 8. C After fixing input nodes in round zero, distinguishing node sizes are empirically bound by ${\log }_{2}r$. Compare to Fig. 7.