Knots Inside Fractals
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910591182962688 |
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| author | Broden, Joshua Espinosa, Malors Nazareth, Noah Voth, Niko |
| author_facet | Broden, Joshua Espinosa, Malors Nazareth, Noah Voth, Niko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Knots Inside Fractals Broden, Joshua Espinosa, Malors Nazareth, Noah Voth, Niko Geometric Topology General Topology 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. |
| title | Knots Inside Fractals |
| topic | Geometric Topology General Topology |
| url | https://arxiv.org/abs/2409.03639 |