Fang presents a new method of generating empires for local vertex configurations in quasicrystals.
She introduces the concept of the empire problem in quasicrystals and its important application in modeling non-local particle interaction in physics. Two old methods of generating the empire of the Penrose tiling are briefly introduced. And a new method, the cut-and-project method, along with its advantages compared with the two old methods, are introduced and discussed in more detail.
