FRACTAL DIMENSION: BOX DIMENSION, HAUSDORFF DIMENSION, AND POTENTIAL THEORY
The concept of dimension has many aspects and meanings in mathematics, and there are a number of dierent denitions of the dimension of a set. In this thesis, 2 denitions of fractal dimension will be discussed, i.e. box-dimension and Hausdor dimension. The relation between box-dimension and Hausdo...
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id-itb.:163592017-09-27T14:41:42ZFRACTAL DIMENSION: BOX DIMENSION, HAUSDORFF DIMENSION, AND POTENTIAL THEORY ANESTASIA , MARIA Indonesia Theses Box dimension, Hausdor dimension, Mass Distribution Principle, Potential Theoretic Method INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/16359 The concept of dimension has many aspects and meanings in mathematics, and there are a number of dierent denitions of the dimension of a set. In this thesis, 2 denitions of fractal dimension will be discussed, i.e. box-dimension and Hausdor dimension. The relation between box-dimension and Hausdor dimension, and methods to determine upper bound and lower bound of Hausdor dimension will also be studied. In the last part, examples of how to apply mass distribution principle and potential theory to determine the lower bound will be given on middle third Cantor set and Cantor dust. text |
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The concept of dimension has many aspects and meanings in mathematics, and there
are a number of dierent denitions of the dimension of a set. In this thesis, 2 denitions
of fractal dimension will be discussed, i.e. box-dimension and Hausdor dimension. The
relation between box-dimension and Hausdor dimension, and methods to determine upper
bound and lower bound of Hausdor dimension will also be studied. In the last part,
examples of how to apply mass distribution principle and potential theory to determine
the lower bound will be given on middle third Cantor set and Cantor dust. |
| format |
Theses |
| author |
ANESTASIA , MARIA |
| spellingShingle |
ANESTASIA , MARIA FRACTAL DIMENSION: BOX DIMENSION, HAUSDORFF DIMENSION, AND POTENTIAL THEORY |
| author_facet |
ANESTASIA , MARIA |
| author_sort |
ANESTASIA , MARIA |
| title |
FRACTAL DIMENSION: BOX DIMENSION, HAUSDORFF DIMENSION, AND POTENTIAL THEORY |
| title_short |
FRACTAL DIMENSION: BOX DIMENSION, HAUSDORFF DIMENSION, AND POTENTIAL THEORY |
| title_full |
FRACTAL DIMENSION: BOX DIMENSION, HAUSDORFF DIMENSION, AND POTENTIAL THEORY |
| title_fullStr |
FRACTAL DIMENSION: BOX DIMENSION, HAUSDORFF DIMENSION, AND POTENTIAL THEORY |
| title_full_unstemmed |
FRACTAL DIMENSION: BOX DIMENSION, HAUSDORFF DIMENSION, AND POTENTIAL THEORY |
| title_sort |
fractal dimension: box dimension, hausdorff dimension, and potential theory |
| url |
https://digilib.itb.ac.id/gdl/view/16359 |
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1820745355968380928 |