α = 0.618 (≈ 1/φ)
β = 0
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About Sturmian Words
A Sturmian word is generated by the cutting sequence of a line y = αx + β with irrational slope α. As x increases, we write '0' when crossing a horizontal grid line and '1' when crossing a vertical grid line.
Balance property: For any two factors of the same length, the number of 1s differs by at most 1.
Complexity: Exactly n+1 distinct factors of length n (minimal for aperiodic sequences).
0.618
Frequency of 1s
Yes
Balanced
n+1
Complexity σ(n)
∞
Period