A ‘vampire einstein’ tile outdoes mathematicians’ latest feat

Sunday, June 4, 2023 - 06:43 in Physics & Chemistry

Einstein, meet “vampire einstein.” It’s been just months since researchers reported the first  “einstein” — a single tile that can cover an infinite plane, but only with a pattern that never repeats (SN: 3/24/23). Now, the same team has found a shape that’s even more special. The original einstein, nicknamed “the hat,” made a pattern that involved both the hat and its mirror image. The new tile also makes a pattern that never repeats, but without such reflections, the researchers report May 28 at arXiv.org. Because the shape isn’t accompanied by its reflection, you might call it a “vampire einstein,” the researchers point out. (The “einstein” part of the name comes from the German for “one stone,” not from the name of the famous physicist.) The shape is part of a family of vampire einsteins that the researchers found, which they called “spectres.” Describing how tiles cover an infinite plane without any overlaps...

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