Growth of a One Dimensional Quasiperiodic Covering with Locally Determined Decorations

Abstract

A growth mechanism for a perfect one-dimensional (1D) quasiperiodic structure is presented with a local covering rule. We use rectangular tiles with two different types of string decorations. The string position in a tile is allowed to move when the tile is attached to an existing patch. By adjusting the position properly with local information, we show that a growth of perfect quasiperiodic structure is possible. This observation may provide new insight into how quasicrystals grow with perfect quasiperiodic order.