Yeesh, we should all remember the von Neumann quip "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." Tha

Yeesh, we should all remember the von Neumann quip "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." That certainly applies to rule 30. There is a deep mathematical theory of random sequences in which this stuff is not random at all. "Kolmogorov randomness" (incompressibility by any Turing machine) is "1-random", but beyond that there is 2-random, 3-random, etc. (incompressibility by machines with higher order halting orders), up through the countable transfinite ordinals if I understand it right. The book "Algorithmic Randomness and Complexity" by Downey and Hirschfeldt goes into all of this. It is way beyond this rule 30 stuff.