A chiral aperiodic monotile
arxiv.org
A chiral aperiodic monotile
1–10 of 83 posts
Re: A chiral aperiodic monotile
#2The recently discovered 2D "hat" monotile tiles aperiodically but allows reflections (and must allow reflections to tile?).
The paper discusses a (2D) monotile whose shape will allow an aperiodic tiling without reflections.
Re: A chiral aperiodic monotile
#3Can anyone explain why people are interested in tilings?
Re: A chiral aperiodic monotile
#4Can anyone explain why people are interested in tilings?
1. Its fairly pure math that you can see
2. Its important in technology and science (e.g quasi crystals).
3. They have an aesthetic some find pleasing.
Re: A chiral aperiodic monotile
#5Can anyone explain why people are interested in tilings?
Tilings are easy to understand and relate to... you can tile your bathroom floor with them for example. Despite that superficial banality, it turns out that it takes a lot of mathematical cleverness to construct and analyze them fully. This particular result is one that people have been chasing for decades and has involved some of the smartest mathamaticians in the world, including Conway and Penrose.
Re: A chiral aperiodic monotile
#6The recently discovered 2D "hat" monotile tiles aperiodically but allows reflections (and must allow reflections to tile?). The paper discusses a (2D) monotile whose shape will allow an aperiodic tiling without reflections.
Notably, it's the same authors: David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss
Re: A chiral aperiodic monotile
#7Can anyone explain why people are interested in tilings?
Tilings are easy to understand and relate to... you can tile your bathroom floor with them for example. Despite that superficial banality, it turns out that it takes a lot of mathematical cleverness to construct and analyze them fully. This particular result is one that people have been chasing for decades and has involved some of the smartest mathamaticians in the world, including Conway and Penrose.
I see thanks. I guess, hearing about other famous hard problems, I am used to seeing comments like: “if problem X could be solved it would unlock lots of other important areas of math.” Wondering if this tiling area draws attention for its own sake alone or if the problems here are similarly vectors to attack larger issues.
Re: A chiral aperiodic monotile
#8Hmmm... I wonder if these spectres are potentially a basis for a new form of cryptographic algorithms. Unique non-repeating sequences exclusively derived from a set of rules and an initial state in multiple dimensions sounds like a promising candidate.
Re: A chiral aperiodic monotile
#9I wonder if the authors anticipated this result when publishing their first paper, or if they were primarily motivated by "complaints" that their hat tile (and other tiles in the associated spectrum) required reflection. Certainly they mention this question, but my question is whether they completely anticipated it.
Re: A chiral aperiodic monotile
#10Can anyone explain why people are interested in tilings?
One of the things this has consequences on are the physics of crystals and pseudocrystals.