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arXiv · 2409.03639

Knots Inside Fractals

Joshua Broden·Malors Espinosa·Noah Nazareth·Niko Voth
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Abstract

We prove that all knots can be embedded into the Menger Sponge fractal. We prove that all Pretzel knots can be embedded into the Sierpinski Tetrahedron. Then we compare the number of iterations of each of these fractals needed to produce a given knot as a mean to compare the complexity of the two fractals.

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Joshua Broden, Malors Espinosa, Noah Nazareth, Niko Voth. 2024-09-05. Knots Inside Fractals. https://arxiv.org/abs/2409.03639

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