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Exterior dimension of fat fractalsGeometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.
Document ID
19850059521
Document Type
Reprint (Version printed in journal)
Authors
Grebogi, C. (Maryland Univ. College Park, MD, United States)
Mcdonald, S. W. (Maryland Univ. College Park, MD, United States)
Ott, E. (Maryland Univ. College Park, MD, United States)
Yorke, J. A. (Maryland, University College Park, United States)
Date Acquired
August 12, 2013
Publication Date
July 1, 1985
Publication Information
Publication: Physics Letters
Volume: 110A
ISSN: 0375-9601
Subject Category
PHYSICS (GENERAL)
Funding Number(s)
CONTRACT_GRANT: NSF MC-81-17967
CONTRACT_GRANT: NSF PHY-82-17853
Distribution Limits
Public
Copyright
Other