Sponsor
Portland State University. Department of Physics
Advisor
Carl Bachhuber
Date of Award
1991
Document Type
Thesis
Degree Name
Master of Science (M.S.) in Physics
Department
Physics
Physical Description
1 online resource (74 p.)
Subjects
Chaotic behavior in systems, Fractals
DOI
10.15760/etd.6066
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, Dfracta1=1.26, none appeared to converge to the fractal dimension.
Persistent Identifier
http://archives.pdx.edu/ds/psu/24078
Recommended Citation
Lindquist, Roslyn Gay, "The dimension of a chaotic attractor" (1991). Dissertations and Theses. Paper 4182.
https://pdxscholar.library.pdx.edu/open_access_etds/4182
10.15760/etd.6066
Description
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