Eigenvalues.
Each state has two ancestors, the square of this number is 4; N has the
minimum sum possible which is 8. Eigenvalues are readily calculated; 
is a unit matrix, as is its tensor square which
commutes with 
. 
has eigenvalues 
; its tensor
square their products in various combinations, so that altogether N has eigenvalues
0 and 2; indeed it is essentially (projectively) idempotent since 
. This is the least rate of increase possible for any 
rule, conforming to the fact that every configuration
of Rule 6 has exactly two ancestors.
Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx