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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