✦ LIBER ✦

Effective fractal dimensions

✍ Scribed by Jack H. Lutz

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 154 KB
Volume: 51
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200310127

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

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)

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