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A NOTE ON APERIODIC AMMANN TILES SHIGEKI AKIYAMA
 

Summary: A NOTE ON APERIODIC AMMANN TILES
SHIGEKI AKIYAMA
Abstract. We present a variant of Ammann tiles consisting of two
similar rectilinear hexagons with edge subdivision, which can tile the
plane but only in non periodic ways. A special matching rule, ghost
marking, plays a key role in the proof.
We shall show that the set of tiles in Figure 1 is aperiodic, that is, it tiles
the plane but only in non periodic way.
1
1
1 c2
c 1 c
1
1 c2
1 c
1
c
1 c
c
1

  

Source: Akiyama, Shigeki - Department of Mathematics, Niigata University

 

Collections: Mathematics