Infinite constant gap length trees in products of thick Cantor sets
Classical Analysis and ODEs
2024-11-20 v2
Abstract
We show that products of sufficiently thick Cantor sets generate trees in the plane with constant distance between adjacent vertices. Moreover, we prove that the set of choices for this distance has non-empty interior. We allow our trees to be countably infinite, which further distinguishes this work from previous results on patterns in fractal sets. This builds on the authors' previous work on graphs and distance sets of products of Cantor sets of sufficient Newhouse thickness.
Cite
@article{arxiv.2211.10750,
title = {Infinite constant gap length trees in products of thick Cantor sets},
author = {Alex McDonald and Krystal Taylor},
journal= {arXiv preprint arXiv:2211.10750},
year = {2024}
}