Finally, something cool. Breakthrough in tiles.

Never mind the politics bullshit, this is actually interesting.

Previously, the least number of shapes required to tile a 2 dimensional plane with non-repeating patterns was two. Sir Roger Penrose invented his Penrose Tiles in 1974. They have a fivefold symmetry, which is supposed to be impossible in mathematics. They assemble to an infinite space and the patterns never repeat. Infinitely variable.

So now there has been discovered a SINGLE shape that does the same thing.

 

The Hat.

 

A quartet of mathematicians from Yorkshire University, the University of Cambridge, the University of Waterloo and the University of Arkansas has discovered a 2D geometric shape that does not repeat itself when tiled. David Smith, Joseph Samuel Myers, Craig Kaplan and Chaim Goodman-Strauss have written a paper describing how they discovered the unique shape and possible uses for it. Their full paper is available on the arXiv preprint server.

When people tile their floors, they tend to use simple geometric shapes that lend themselves to repeating patterns, such as squares or triangles. Sometimes though, people want patterns that do not repeat but that represents a challenge if the same types of shape are used. In this new effort, the research team has discovered a single geometric shape that if used for tiling, will not produce repeating patterns.

This, believe it or not, is a Big Deal. A completely novel way to tile the 2D plane with no repeating patterns. Amazing.

You're welcome. ~:D