I am working on projects in solving ground state of generalized ising models. One recent work involves tiling with basic tiles that filled the whole lattice. For example, we could obtain results: ...
This is perhaps a vague question, but hopefully there exists literature on the subject. The question is motivated by an answer I gave to this question on math.SE. There exists a rather remarkable ...
Let $\cal C = \lbrace C_i \rbrace$ be a collection of rectifiable curves in the plane with the property that every unit-length segment meets at least one curve in at least one point. Call such a ...
I want to study quasicrystals from mathematical point of view, but I'm having hard time finding materials about it. If you could suggest me some books, articles or papers, I would be glad.
Hello MO, I've been working on a problem I'm working on in ergodic theory (finding Alpern lemmas for measure-preserving $\mathbb R^d$ actions) and have found some neat tilings, that I presume were ...
Can anyone suggest a survey (or surveys) that provides an update to Tilings and Patterns by Grunbaum and Shepard? If there's a more recent book, that would be fantastic, but I don't see one. I am ...
I am looking for a copy of the following W. Thurston, Groups, tilings, and finite state automata, AMS Colloquium Lecture Notes. I see that a lot of papers in the tiling literature refer to it but I ...