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Effective fractal dimensions
Author(s) -
Lutz Jack H.
Publication year - 2005
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310127
Subject(s) - fractal , computability , mathematics , hausdorff dimension , fractal dimension , dimension (graph theory) , hausdorff space , computability theory , discrete mathematics , pure mathematics , mathematical analysis
Classical fractal dimensions (Hausdorff dimension and packing dimension) have recently been effectivized by (i) characterizing them in terms of real‐valued functions called gales, and (ii) imposing computability and complexity constraints on these gales. This paper surveys these developments and their applications in algorithmic information theory and computational complexity theory. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)