To see how the mean field theory supplies a parameterization
of cellular automata, we rewrite equation 1 as follows.
First note that only blocks B which lead to a 1 under the
rule contribute to the sum on the r.h.s. of equation 1.
Second note that two blocks B and 
such that 
contribute
to the sum in exactly the same way. Let 
be the number
of blocks which contribute to the sum and contain i cells in state 1.
Then equation 1 is written
All cellular automata with the same coefficient values 
have the same
behavior in mean field approximation. A cellular automaton which
gives rise to the coefficient values 
is said to occupy the
mean field class determined by 
.
Improvement of the mean field theory requires that the assumption that no correlations between cell states are generated by cellular automata be relaxed. A sequence of generalizations [GVK87]. of the mean field theory has been devised in which correlations are represented in terms of the probability of blocks of length l. In the following, we will use 2nd and 10th order mean field theory to approximate the behavior of rules. Thus, correlations included in the probability of blocks of size 2 or 10 respectively are included in the calculations.