Forcing nonperiodicity with a single tile

Details Forcing nonperiodicity with a single tile Forcing nonperiodicity with a single tile

2010-09-07

arxiv.org/abs/1009.1419v2

Mathematics

Combinatorics

18 pages, 10 figures. This article has been substantially revised and accepted for publication in the Mathematical Intelligenc

Scientific paper

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 prototile we recently introduced that is an einstein according to a reasonable definition. [This abstract does not appear in the published article.]

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