To define 
, we consider CA
with a symmetric quiescent condition (homogeneous neighborhoods do not
change), and we arbitrarily pick one of the states
and call it the reference state 
. If we let P(
) be
the percentage of transitions to state 
in the rule table,
then we define the parameter 
as: 
.
We now use 
to generate random CA transition rules as follows. Pick
a value
for 
and divide the remaining probability of 
equally among the remaining states. Walk through the rule table filling in
the transitions using these probabilities. Thus, for 
, all
the transitions save the non-
homogeneous neighborhoods will be
to state 
, for 
, half of the transitions will be
to state 
and the remaining transitions will be equally distributed
among the other states, and for 
, none of the transitions
will be to 
, and the other states will be represented equally in the
transition table. Twisting the 
knob generating a series of transition
rules and studying the behavior of CA run under the rule-tables so-generated
is a simple way to search for structure and interesting regions in CA
rule-space. Previous work has shown that 
serves to isolate
regions of rule space in which dynamically simple or complex rules
are located. 
is a crude measure of the behavior of
CA; rules with identical 
may have widely different behavior.
The approach taken here is to limit the variability of behavior
by using a set of parameters, the mean field parameters,
which refine the 
parameter.