  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.
