平面镶嵌的弱色局部规则
Weak colored local rules for planar tilings
摘要：
如果存在一个有限的修饰图块集，其平铺是$E$的数字化，则$\mathbb{R}^n$的线性子空间$E$具有着色局部规则.如果数字化可以稍微在$E$周围徘徊，则局部规则是弱的。我们证明了线性子空间具有弱色局部规则当且仅当它是可计算的。这超越了以前的结果，所有基于代数子空间。我们证明了一个类似的特征集的线性子空间，包括集的所有线性子空间的$\mathbb{R}^n$。
英文摘要：
A linear subspace $E$ of $\mathbb{R}^n$ has colored local rules if there exists a finite set of decorated tiles whose tilings are digitizations of $E$. The local rules are weak if the digitizations can slightly wander around $E$. We prove that a linear subspace has weak colored local rules if and only if it is computable. This goes beyond the previous results, all based on algebraic subspaces. We prove an analogous characterization for sets of linear subspaces, including the set of all the linear subspaces of $\mathbb{R}^n$.
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