All articles tagged with #aperiodic tiling
Computer scientists have discovered a new aperiodic tile called "Spectre" that can completely cover a flat surface without repeating a specific pattern. This kind of tiling has been a tricky problem in mathematics for a long time. The previously discovered "Einstein" tile was considered a one-in-a-million shape, but Spectre is an even rarer discovery.
A tiny, hat-shaped polygon called the "einstein" has been discovered by a team of researchers led by nonprofessional mathematician David Smith. The shape can tessellate with itself in such a way that it can cover an infinite surface without ever creating a repeating pattern, making it the first known single-tile aperiodic tiling. Aperiodic tilings are important in the development of quasicrystals, which have found applications in everything from Kleenexes to real-life Terminator-style robots.
Mathematicians have identified a 13-sided shape called "the hat" that can tile a surface without repeating, making it an aperiodic monotile. The hat is a polykite shape consisting of eight kites connected at their edges. The existence of an aperiodic monotile was purely theoretical until a research team led by mathematician David Smith and colleagues proved its existence in a preprint paper posted online this month. The discovery appears to answer a long-standing question in the field of geometry.