UNSPECIFIED (2002) The Hausdorff dimension of some snowflake-like recursive constructions. Nature, 10 (2). pp. 199-208. ISSN 0218-348X

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Abstract

Fractal subsets of R-n with a highly regular structure are often constructed as a limit of a recursive procedure based on contractive maps. The Hausdorff dimension of recursively constructed fractals is relatively easy to find when the contractive maps associated with each recursive step satisfy the Open Set Condition (OSC). We present a class of random recursive constructions which resemble snowflake structures and which break the OSC. We calculate the associated Hausdorff dimension and conjecture that an a.s. deterministic exact Hausdorff function does not exist.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science
Journal or Publication Title:	Nature
Publisher:	WORLD SCIENTIFIC PUBL CO PTE LTD
ISSN:	0218-348X
Date:	June 2002
Volume:	10
Number:	2
Number of Pages:	10
Page Range:	pp. 199-208
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/10776

Data sourced from Thomson Reuters' Web of Knowledge

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