The dimension of a chaotic attractor
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-Procacc...
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| Format: | Others |
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PDXScholar
1991
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| Online Access: | https://pdxscholar.library.pdx.edu/open_access_etds/4182 https://pdxscholar.library.pdx.edu/cgi/viewcontent.cgi?article=5192&context=open_access_etds |
| Summary: | 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. |
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