This paper first discusses the size and orientation of hat supertiles. Fibonacci and Lucas sequences, as well as a third integer sequence linearly related to the Lucas sequence are involved. The result is then generalized to any aperiodic tile in the hat family.

翻译：本文首先讨论了帽子超平铺的尺寸与取向。该过程涉及斐波那契数列、卢卡斯数列以及与卢卡斯数列呈线性相关的第三个整数序列。随后，这一结论被推广至帽子族中的任意非周期镶嵌单元。