= Characteristic Sturmian word
For an <irrational number> $0<\alpha<1$, the <characteristic Sturmian word> of slope $\alpha$ is the binary <sequence>
$$
c_\alpha(n)=\lfloor(n+2)\alpha\rfloor-\lfloor(n+1)\alpha\rfloor,\qquad n\ge0.
$$
Each term is zero or one because the arguments differ by less than one. This fixes an intercept convention: it is the lower mechanical word with intercept $\alpha$.
For $\alpha=(3-\sqrt5)/2$, the beginning is $0100101001\ldots$, the <Fibonacci word>. Like every <Sturmian word>, it has exactly $n+1$ distinct factors of length $n$. Its relation to <continued fractions> makes its recursive block structure reflect the partial quotients of its slope.
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