Non-repeating Tiling Shape Found

[robcat2075]

In yet another sign of the Apocalypse, someone has invented a shape that can be tiled with itself, but will not create repeating patterns.

Elusive ‘Einstein’ Solves a Longstanding Math Problem

 

Quote

...an einstein is an “aperiodic monotile,” a shape that tiles a plane, or an infinite two-dimensional flat surface, but only in a nonrepeating pattern. (The term “einstein” comes from the German “ein stein,” or “one stone” — more loosely, “one tile” or “one shape.”) Your typical wallpaper or tiled floor is part of an infinite pattern that repeats periodically; when shifted, or “translated,” the pattern can be exactly superimposed on itself. An aperiodic tiling displays no such “translational symmetry,” and mathematicians have long sought a single shape that could tile the plane in such a fashion. This is known as the einstein problem.