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Bounds on the
Hausdorff measure of level-$N$ Sierpinski gaskets
Andrea Arauza Rivera and Edwin Lin
Vol. 15 (2022), No. 3, 379–391
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Abstract |
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Although a favorite of fractal geometers, the Hausdorff measure of many classical fractals is often difficult to calculate or even bound. We review some important definitions and results from fractal geometry and define the fractal known as the level- Sierpinski gasket. By generalizing a previous technique used for the classical Sierpinski gasket, the main result of this work obtains an upper bound for the Hausdorff measure of the level- Sierpinski gasket. |
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Keywords
fractal, fractals, Hausdorff measure, Sierpinski gasket,
Hausdorff dimension
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Mathematical Subject Classification
Primary: 11K55, 28A78, 28A80, 37F35
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Milestones
Received: 28 July 2020
Revised: 9 August 2021
Accepted: 2 January 2022
Published: 2 December 2022
Communicated by Kenneth S. Berenhaut
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Authors |
| Andrea Arauza Rivera | |
| Department of Mathematics California State University, East Bay Hayward, CA United States |
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| Edwin Lin | |
| Department of Mathematics University of California Riverside, CA United States |
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