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