Buffon needles landing near Sierpinski gasket
Matthew Bond, Alexander Volberg
TL;DR
This paper estimates the probability of Buffon needles landing near a Sierpinski gasket, extending previous methods to fractal sets with Hausdorff dimension 1.
Contribution
It adapts Nazarov, Peres, and Volberg's approach to provide an upper bound for Buffon needle probability on the Sierpinski gasket.
Findings
Provides an upper estimate for Buffon needle probability on the gasket.
Extends existing methods to fractals with Hausdorff dimension 1.
Offers insights into geometric probability on complex fractal structures.
Abstract
In this paper we modify the method of Nazarov, Peres, and Volberg "The power law for the Buffon needle probability of the four-corner Cantor set", arXiv:0801.2942, to get an estimate from above of the Buffon needle probability of the --th partially constructed Sierpinski gasket of Hausdorff dimension 1.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · Digital Image Processing Techniques