Sponsor
Portland State University. Department of Physics
First Advisor
Carl Bachhuber
Term of Graduation
Spring 1991
Date of Publication
5-28-1991
Document Type
Thesis
Degree Name
Master of Science (M.S.) in Physics
Department
Physics
Language
English
Subjects
Chaotic behavior in systems, Fractals
DOI
10.15760/etd.6066
Physical Description
1 online resource (2, iv, 66 pages)
Abstract
Tools to explore chaos are as far away as a personal computer or a pocket calculator. A few lines of simple equations in BASIC produce fantastic graphic displays. In the following computer experiment, the dimension of a strange attractor is found by three algorithms; Shaw's, Grassberger-Procaccia's and Guckenheimer's. The programs were tested on the Henon attractor which has a known fractal dimension. Shaw's and Guckenheimer's algorithms were tested with 1000 data points, and Grassberger's with 100 points, a data set easily handled by a PC in one hour or less using BASIC or any other language restricted to 640K RAM. Since dimension estimates are notorious for requiring many data points, the author wanted to find an algorithm to quickly estimate a low-dimensional system (around 2). Although all three programs gave results in the neighborhood of the fractal dimension for the Henon attractor, Dfractal=1.26, none appeared to converge to the fractal dimension.
Rights
In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
Persistent Identifier
https://archives.pdx.edu/ds/psu/24078
Recommended Citation
Lindquist, Roslyn Gay, "The Dimension of a Chaotic Attractor" (1991). Dissertations and Theses. Paper 4182.
https://doi.org/10.15760/etd.6066
Comments
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