Figure 2

A spectral gap and level sets reveal the genetic code. Eigenvalues of the codon substitution transition matrix P (note that the system has 61 states as substitutions from the three stop codons are not considered). A distinct spectral gap after the 21st first eigenvalues (marked in red) suggests that the 21 first eigenvectors reveal an aggregation. (b) Vector elements of the fourth eigenvector of P are organized in level sets, where codons that map to the same amino acid are on the same level (with the exception of serine). All the eigenvalues are real because the transition matrix P is reversible.