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