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.