Is the whole paper just this one page that's visible to me, or is there more? This is a classic physics FAQ type question!
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the inclusion takes any stage m greater than n, and includes n in it the blurrier one says "blur any two stages, they resemble one another". both of these can, for the related power series, amount to explicit operations upon them
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for what it's worth: my current aim with these (generally) is to build something to distinguish bifurcation cascades in the 4.669.. universality class by looking at infinite products analogous to the ones for automatic groups. (Rostislov Grigorchuk might be worth a look)
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Read the paperfolding paper to start.
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This was today: https://arxiv.org/abs/1910.07399 /The Thue-Morse shift, Baumslag-Solitar group, and biminimality/ Laurent Bartholdi
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