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$s_{n+1}=s_n^2-s_{n-1}^2$, $s_0=\sqrt{x}$, $s_1=x$ This sequence seems simple, but is pretty confusing. If you try it with integers, you might think that it always diverges to infinity, but if you try ...

Let $z$ be a fixed complex number with $|z|<1$ and consider the set $$X_z := \Big\{\sum\limits_{i=1}^{\infty} a_i z^i \ \Big|\ a_i\in \{-1,1\} \forall i\Big\}.$$ What can be said about the set $M$ ...