Block variables for deterministic aperiodic sequences

We use the concept of block variables to obtain a measure of order/disorder for some one-dimensional deterministic aperiodic sequences. For the Thue - Morse sequence, the Rudin - Shapiro sequence and the period-doubling sequence it is possible to obtain analytical expressions in the limit of infinite sequences. For the Fibonacci sequence, we present some analytical results which can be supported by numerical arguments. It turns out that the block variables show a wide range of different behaviour, some of them indicating that some of the considered sequences are more `random' than other. However, the method does not give any definite answer to the question of which sequence is more disordered than the other and, in this sense, the results obtained are negative. We compare this with some other ways of measuring the amount of order/disorder in such systems, and there seems to be no direct correspondence between the measures.

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