Knots Inside Fractals
Geometric Topology
2024-09-06 v1 General Topology
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.
Keywords
Cite
@article{arxiv.2409.03639,
title = {Knots Inside Fractals},
author = {Joshua Broden and Malors Espinosa and Noah Nazareth and Niko Voth},
journal= {arXiv preprint arXiv:2409.03639},
year = {2024}
}
Comments
14 pages