Abstract:
Motivated by the Ducci Map and Wolfram's Rule 90, this paper studies the
relationship of the period lengths of the maps
as a function of and , where is the identity map and is the left shift map on . It is found that is conjugate to for . A closed form expression for the minimal polynomial
of is obtained. In addition, using the language of
minimal polynomials, we find that when ,the period lengths of are equal to the period lengths of where
.
as a function of 
and 
, where 
is the identity map and 
is the left shift map on 
. It is found that 
is conjugate to 
for 
. A closed form expression for the minimal polynomial
of 
,the period lengths of 
where
.