This letter demonstrates that the mean field classification agrees on average with the Wolfram classification where statistical properties of cellular automata are concerned. The mean field classification has several advantages over the Wolfram classification. 1) Assignment of cellular automata to mean field classes is simply decided, while Wolfram class membership is undecidable[9]. 2) Construction of all members of a mean field class is straight-forward, while no method is known to find all members of a Wolfram class. 3) Solution of the mean field equations produces quantitative estimates both for invariant probability measures and the stability of these measure, while the Wolfram classification is qualitative in this regard. 4) The mean field theory contains parameters whose smooth variation typically results in smooth variation of the properties of the corresponding rules, while the Wolfram classification is not parametric. 5) The mean field classification may be systematically refined to take longer-range correlations into account[7][5], while the Wolfram classification contains but four "universal"[1] classes.
Largest stable fixed point for mean field equations
for r=1 rules. 
and 
vary
between 0 and 3, while 
varies between 0 and 1.
The shading gives 
evaluated
at the fixed point. Black, white,
correspond to = 0, 1 respectively.
Heavy solid line: stable fixed points of 
and iterates of
for r=3
rules. Light solid line:
average density of rules in mean field classes determined by 
(error bars give
1 standard
deviation).
Background: fraction of rules in each mean field class which exhibit various Wolfram
class behaviors.