Quasiperiodic Patterns

Abstract

We present here a general framework to produce quasiperiodic tilings and more general quasiperiodic patterns in $n$ dimensions corresponding to a finite number of local neighborings around each point. In particular, we give simple descriptions of the Penrose tilings of the plane and of a tiling of the three-dimensional space which exhibits an icosahedral symmetry. The Fourier transform of this last pattern is derived and shows a striking similarity with the electron-diffraction images obtained for a recently discovered alloy of Al and Mn.