Empirical Study of Minkowski-Bouligand and Hausdorff-Besicovitch Dimensions of Fractal Curves
The properties of entities uncovered along the area of fractal geometry are appealing. A relatively short algorithm can produce complex shapes. The fractals find use in many areas, like animation, simulation, computer graphics, algorithms, and more. We use the fractal geometry mostly, but not limite...
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| Veröffentlicht in: | 2019 17th International Conference on Emerging eLearning Technologies and Applications (ICETA) S. 231 - 238 |
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| 1. Verfasser: | |
| Format: | Tagungsbericht |
| Sprache: | Englisch |
| Veröffentlicht: |
IEEE
01.11.2019
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | The properties of entities uncovered along the area of fractal geometry are appealing. A relatively short algorithm can produce complex shapes. The fractals find use in many areas, like animation, simulation, computer graphics, algorithms, and more. We use the fractal geometry mostly, but not limited to, to teach algorithm, specifically the recursion. This article uncovers the possibilities to specify and compare the Hausdorff-Besicovitch and Minkowski-Bouligand dimension of fractal curves using empirical methods even for the Hausdorff-Besicovitch dimension using the method we did not notice to be used in other sources that we disclosed. In the first part, we analyze a few well-known fractal curves; eventually, we investigate the properties of the unique fractal curve (with a working name curly fractal curve"). The last curve became the subject of our interest because of its features shown while we processed the data about it. Further, a more in-depth investigation would be needed to explain some of them. |
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| DOI: | 10.1109/ICETA48886.2019.9040005 |