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Sturmian Sequence

If a Sequence has the property that the Block Growth function $B(n) = n+1$ for all $n$, then it is said to have minimal block growth, and the sequence is called a Sturmian sequence. An example of this is the sequence arising from the Substitution Map

$\displaystyle 0$ $\textstyle \to$ $\displaystyle 01$  
$\displaystyle 1$ $\textstyle \to$ $\displaystyle 0,$  

yielding $0 \to 01 \to 010 \to 01001 \to 01001010 \to \ldots$, which gives us the Sturmian sequence 01001010....

Sturm Functions are sometimes also said to form a Sturmian sequence.

See also Sturm Function, Sturm Theorem

© 1996-9 Eric W. Weisstein