论文标题
右金三角的飞机非周期性瓷砖的家族
A family of non-periodic tilings of the plane by right golden triangles
论文作者
论文摘要
我们研究了一个具有相似右三角形相似的替代瓷砖家庭，这些尺寸使用了[Danzer，L。和Van Ophuysen，G。所引入的替代规则，G。一种平面三角形砖的物种，具有通胀因子$ \ sqrt { - τ} $。 res。公牛。 Panjab大学。科学。 2000，50，1-4，第137--175页（2001）]。在该论文中，可以证明，可以使用装饰的瓷砖从当地规则中获得这个瓷砖系列。也就是说，这个家庭是\ emph {sofic}。 在本文中，我们提供了这一事实的替代证明。我们使用的瓷砖比Danzer和Van Ophuysen（22代替10）。但是，我们对超级物品的装饰更加直观，我们的本地规则更为简单。
We study a family of substitution tilings with similar right triangles of two sizes which is obtained using the substitution rule introduced in [Danzer, L. and van Ophuysen, G. A species of planar triangular tilings with inflation factor $\sqrt{-τ}$. Res. Bull. Panjab Univ. Sci. 2000, 50, 1-4, pp. 137--175 (2001)]. In that paper, it is proved this family of tilings can be obtained from a local rule using decorated tiles. That is, that this family is \emph{sofic}. In the present paper, we provide an alternative proof of this fact. We use more decorated tiles than Danzer and van Ophuysen (22 in place of 10). However, our decoration of supertiles is more intuitive and our local rule is simpler.
