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Randomness and Effective Dimension of Continued Fractions Nandakumar, Satyadev Vishnoi, Prateek Continued fractions Martin-Löf randomness Computable randomness effective Fractal dimension Recently, Scheerer [Adrian-Maria Scheerer, 2017] and Vandehey [Vandehey, 2016] showed that normality for continued fraction expansions and base-b expansions are incomparable notions. This shows that at some level, randomness for continued fractions and binary expansion are different statistical concepts. In contrast, we show that the continued fraction expansion of a real is computably random if and only if its binary expansion is computably random. To quantify the degree to which a continued fraction fails to be effectively random, we define the effective Hausdorff dimension of individual continued fractions, explicitly constructing continued fractions with dimension 0 and 1. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Satyadev Nandakumar and Prateek Vishnoi 2020 Is Part Of LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2020.73 urn:nbn:de:0030-drops-127424 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.73 eng https://creativecommons.org/licenses/by/3.0/legalcode