Chapter 6: Starting from Randomness

Section 2: Four Classes of Behavior

Undecidability [of cellular automaton classes]

Almost any definite procedure for determining the class of a particular rule will have the feature that in borderline cases it can take arbitrarily long, often formally showing undecidability, as discussed on page 1138. (An example would be a test for class 1 based on checking that no initial pattern of any size can survive. Including probabilities can help, but there are still always borderline cases and potential undecidability.)

From Stephen Wolfram: A New Kind of Science [citation]