Eigenvalues.
Evidently this rule gives 0 one ancestor, 1 three. Their squares are 1
and 9, visible respectively as the number of nonzero elements in the individual
tensor products. The element sum of N is 10; its eigenvalues are 
, 
,
contrasted to eigenvalues 0, 1 for 
and 
for 
.
The 
configurations of length n will
have 
ancestors for an average of 4 each,
while the sum of the squares of the number of ancestors will eventually grow according to 
. The growth could be as small as a factor of 2
per cell or as large as a factor of 4, according to whether all configurations have
an equal number of ancestors, or all ancestors map into a single configuration.
The quiescent state will have asymptotically 
ancestors (whose square is 
), an increasingly
negligible proportion.
Because the mean is always constant and small, the variance, 
, will grow asymptotically at half (square root) the rate of the second
moment, or by 
, or 18% per additional cell.
Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx