Show that orbit of the Thue-Morse sequence is dense in the shift space.

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Show that orbit of the Thue-Morse sequence is dense in the shiftspace.

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Let xx denote the infinite ThueMorse word x0110100110010110x0110100110010110 which is defined as being the only fixed point starting with 00 of the morphism SS defined over the words on the alphabet 0101 given by S001S001 and S110S110 that is xS0limn1Sn0xS0limn1Sn0 this is only one among many different    See Answer
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