Notes

(1) A stricter definition of randomness can be based on the non-existence of simple descriptions [3], rather than merely the difficulty of finding them. None of the sequences discussed here, nor many generally considered random, would qualify according to this definition.

(2) This operation can be performed locally on a base 6 digit sequence, and so can be implemented as a cellular automaton. Given particular finite boundary conditions, it acts like a linear congruential sequence generator (e.g., [1]). But in an infinite region, its behaviour is more complicated, and is related to the so-called problem [9].

(3) Recent results [45] suggest in fact that , yielding a final value of 1.

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