# A Polynomial Time Algorithm for the Hausdorff Dimension of Continued Fraction Cantor Sets

@article{Hensley1996APT,
title={A Polynomial Time Algorithm for the Hausdorff Dimension of Continued Fraction Cantor Sets},
author={Doug Hensley},
journal={Journal of Number Theory},
year={1996},
volume={58},
pages={9-45}
}
• D. Hensley
• Published 1 May 1996
• Mathematics
• Journal of Number Theory
For any finite setAof positive integers, letEA :={α∈(0, 1):αis irrational, and every partial quotient in the (infinite) simple continued fraction expansion ofαis an element ofA}. For setsAwith fewer than two elements,EAis uninteresting. For |A|⩾2,EAis a kind of Cantor fractal dust, with a Hausdorff dimension (dim EA) between 0 and 1. This work presents an algorithm which, given a finite setAof between 2 andNpositive integers 2N, determines dim EAto within ±2−NusingO(N7) elementary bit…
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