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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
Abstract

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-N 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-N Sierpinski gasket.

Keywords
fractal, fractals, Hausdorff measure, Sierpinski gasket, Hausdorff dimension
Mathematical Subject Classification
Primary: 11K55, 28A78, 28A80, 37F35
Milestones
Received: 28 July 2020
Revised: 9 August 2021
Accepted: 2 January 2022
Published: 2 December 2022

Communicated by Kenneth S. Berenhaut
Authors
Andrea Arauza Rivera
Department of Mathematics
California State University, East Bay
Hayward, CA
United States
Edwin Lin
Department of Mathematics
University of California
Riverside, CA
United States