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2000•NonlinearityOpen access

A new estimate of the Hausdorff measure of the Sierpinski gasket

Zuoling Zhou, Feng Li

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Abstract

In this paper, we develop the hexagon method and the dodecagon method to estimate the Hausdorff measure of the Sierpinski gasket and show that the Hausdorff measure of the Sierpinski gasket is upper-bounded by a single-variable continuous function. Better upper bounds of the Hausdorff measure of the Sierpinski gasket are also achieved.

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What this paper is about

In this paper, we develop the hexagon method and the dodecagon method to estimate the Hausdorff measure of the Sierpinski gasket and show that the Hausdorff measure of the Sierpinski gasket is upper-bounded by a single-variable continuous function. Better upper bounds of the Hausdorff measure of the Sierpinski gasket are also achieved.

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Available abstract

In this paper, we develop the hexagon method and the dodecagon method to estimate the Hausdorff measure of the Sierpinski gasket and show that the Hausdorff measure of the Sierpinski gasket is upper-bounded by a single-variable continuous function. Better upper bounds of the Hausdorff measure of the Sierpinski gasket are also achieved.

Key concepts: Sierpinski triangle, Hausdorff measure, Mathematics, Gasket, Measure (data warehouse), Bounded function, Hausdorff space, Hausdorff distance

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