The dimension of the boundary of the Lévy Dragon
In this paper we describe the computations done by the authors in determining the dimension of the boundary of the Lévy Dragon. A general theory was developed for calculating the dimension of a self-similar tile and the theory was applied to this particular set. The computations were challenging. It...
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Hindawi Limited
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000872 |
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doaj-646a5ab19e33462eb78fa684b71e39002020-11-24T21:47:42ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120462763210.1155/S0161171297000872The dimension of the boundary of the Lévy DragonP. Duvall0J. Keesling1Department of Mathematical Sciences, University of North Carolina at Greensboro, Greensboro, NC 27412, USADepartment of Mathematics, University of Florida, P.O Box 118105, 358 Little Hall, Gainesville, FL 32611-8105, USAIn this paper we describe the computations done by the authors in determining the dimension of the boundary of the Lévy Dragon. A general theory was developed for calculating the dimension of a self-similar tile and the theory was applied to this particular set. The computations were challenging. It seemed that a matrix which was 215×215 would have to be analyzed. It was possible to reduce the analysis to a 752×752 matrix. At last it was seen that if λ was the largest eigenvalue of a certain 734×734 matrix, then dimH(K)=ln(λ)ln((2)) Perron-Frobenius theory played an important role in analyzing this matrix.http://dx.doi.org/10.1155/S0161171297000872Hausdorff dimensioniterated function systemsattractorsfractal geometry. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
P. Duvall J. Keesling |
| spellingShingle |
P. Duvall J. Keesling The dimension of the boundary of the Lévy Dragon International Journal of Mathematics and Mathematical Sciences Hausdorff dimension iterated function systems attractors fractal geometry. |
| author_facet |
P. Duvall J. Keesling |
| author_sort |
P. Duvall |
| title |
The dimension of the boundary of the Lévy Dragon |
| title_short |
The dimension of the boundary of the Lévy Dragon |
| title_full |
The dimension of the boundary of the Lévy Dragon |
| title_fullStr |
The dimension of the boundary of the Lévy Dragon |
| title_full_unstemmed |
The dimension of the boundary of the Lévy Dragon |
| title_sort |
dimension of the boundary of the lévy dragon |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1997-01-01 |
| description |
In this paper we describe the computations done by the authors in determining the
dimension of the boundary of the Lévy Dragon. A general theory was developed for calculating the
dimension of a self-similar tile and the theory was applied to this particular set. The computations were
challenging. It seemed that a matrix which was 215×215 would have to be analyzed. It was possible to reduce the analysis to a 752×752 matrix. At last it was seen that if λ
was the largest eigenvalue of a
certain 734×734 matrix, then dimH(K)=ln(λ)ln((2)) Perron-Frobenius theory played an important role
in analyzing this matrix. |
| topic |
Hausdorff dimension iterated function systems attractors fractal geometry. |
| url |
http://dx.doi.org/10.1155/S0161171297000872 |
| work_keys_str_mv |
AT pduvall thedimensionoftheboundaryofthelevydragon AT jkeesling thedimensionoftheboundaryofthelevydragon AT pduvall dimensionoftheboundaryofthelevydragon AT jkeesling dimensionoftheboundaryofthelevydragon |
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1725896273061478400 |