Forcing Nonperiodicity with a Single Tile

  title={Forcing Nonperiodicity 
with a Single Tile},
  author={Joshua E. S. Socolar and Joan M. Taylor},
  journal={The Mathematical Intelligencer},
An aperiodic prototile is a shape for which infinitely many copies can be arranged to fill Euclidean space completely with no overlaps, but not in a periodic pattern. Tiling theorists refer to such a prototile as an "einstein" (a German pun on "one stone"). The possible existence of an einstein has been pondered ever since Berger's discovery of large set of prototiles that in combination can tile the plane only in a nonperiodic way. In this article we review and clarify some features of a… Expand
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