3.3. The function of local rules in an Elementary Cellular Automata
The mapping relation between Nt
x ¼ st
x1; st
x; st
xþ1
(the states of the cell and the neighbors) and Mð1Þ, Mð2Þ can be established
by constructing the function z ¼ f ðst
x; g1; g2. According to the state-transition table of local rules, the elements in
Mð1Þ and Mð2Þ are the states stþ1
x of Nt
x ¼ ðst
x1; st
x; st
xþ1Þ at the moment of t þ 1, as shown in Table 2. Therefore, there is an
analytic function of the local rules for the evolution of the ECA as follows. As a result, we have that: