only for moore and ven... rules
'd'=density for random fillings
'n'=the number after rules(b3=>n=3)
'a'=neighbors
for a birth rule:
the percentage of live cells after a generation:
d^n*(1-d)^(a-n)*((fact(a)/fact(a-n))/fact(n))*(1-d)
for a survival rule:
the percentage of live cells after a generation:
d^n*(1-d)^(a-n)*((fact(a)/fact(a-n))/fact(n))*d
add all things you've calculated, you'll get the cell's living probabilistic for the rule!!!!
p.s. this is my science fair project for junior high
I may post a equation for a limited space a few day's after~