Bounds on the Hausdorff measure of level-N Sierpinski gaskets

Arauza Rivera, Andrea; Lin, Edwin

doi:10.2140/involve.2022.15.379

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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

DOI: 10.2140/involve.2022.15.379

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

Vol. 15, No. 3, 2022