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.