I'm a little bit hesitant to ask this here, so please notice the tag. My hope is that someone will have a more satisfying answer than what I've heard before...


A long time ago I read (perhaps 'browsed' is a better word) Wolfram's "A New Kind of Science". There are many many references to the "Rule 30" CA - <http://mathworld.wolfram.com/Rule30.html>. However, no intuitive reasoning for it's random/pseudorandom behavior is provided prior to a digression to the importance of the discovery. I was recently reminded of this when I heard that Mathematica (a program I use quite frequently) uses certain outputs from this CA as its random number generator. 


So my question is - beyond 'numerical phenomenology' is there an intuitive understanding why Rule 30 should behave in this random/pseudorandom manner?



An intuitive reason why the "Rule 30" CA is random/pseudorandom?
If you look at the [results of elementary cellular automata](http://mathworld.wolfram.com/ElementaryCellularAutomaton.html) from mathworld, most of them seem to have some kind of symmetry. (I don't want to make "symmetry" formal here; what I mean is that you get nice patterns of some sort.)


But I suspect that in general, the results of cellular automata are psuedorandom. (I haven't looked at this too closely.)


So if I had to guess, I would say that the answer is just that most CAs on small neighborhoods are "nice", and most CAs on large neighborhoods aren't. Rule 30 is not sporadic, but it's the first example of a family that eventually predominates. 


