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Spectres

All articles tagged with #spectres

Mathematical breakthroughs: Aperiodic monotiles, improved Einstein, and infinite tiling patterns.

Originally Published 2 years ago — by Phys.org

Mathematicians have discovered a close relative of "the hat," an aperiodic tile that does not repeat itself when tiled, that is a true chiral aperiodic monotile. The new shape, called a Spectre, is strictly chiral and admits only non-periodic tilings even when reflections are permitted. The team found that modifying the edges of the newly discovered polygon in certain ways creates a whole family of shapes, all strictly chiral aperiodic monotiles.

science science aperiodic-tile chiral mathematics monotile science spectres

Mathematicians Crack Decades-Long Tiling Puzzle with Upgraded Einstein Shape

Originally Published 2 years ago — by The New York Times

Researchers have discovered a new-and-improved "einstein" - a single shape that tiles a plane, or an infinite two-dimensional flat surface, but only in a nonrepeating pattern. The new monotile discovery does not use reflections and is a close relative of the original "hat" einstein. The team produced a family of strong or "strictly chiral aperiodic monotiles" through a simple modification of the T(1,1) tile, named "Spectres," which only allow nonperiodic tilings, and without reflections.

science science-and-technology aperiodic-monotile einstein mathematics science-and-technology spectres tiling