At Long Last, Mathematicians Have Found a Pattern That Never Repeats

[pellinore]

From bathroom floors to honeycombs or even groups of cells, tilings surround us. These patterns cover a space without overlapping or leaving any gaps. Like a rug filled with diamond shapes, where each section looks the same as the one next to it, every tiling ever recorded has eventually repeated itself—until now.

After decades of searching for what mathematicians call an “einstein tile”—an elusive shape that would never repeat—researchers say they have finally identified one. The 13-sided figure is the first that can fill an infinite surface with a pattern that is always original.

At Long Last, Mathematicians Have Found a Shape With a Pattern That Never Repeats | Smart News| Smithsonian Magazine

Edited April 1 by pellinore

[Sir Wearer of Hats]

And….. we take another step closer to summoning the eldritch, non-Euclidean horrors from beyond the angle we can never perceive except in nightmares.

[Alchopwn]

Just now, Sir Wearer of Hats said:

And….. we take another step closer to summoning the eldritch, non-Euclidean horrors from beyond the angle we can never perceive except in nightmares.

Massachusetts Lovecraft Country kids: "Are we there yet?"

[Alchopwn]

31 minutes ago, pellinore said:

After decades of searching for what mathematicians call an “einstein tile”—an elusive shape that would never repeat—researchers say they have finally identified one. The 13-sided figure is the first that can fill an infinite surface with a pattern that is always original.

I am going to enjoy reading the paper that proves this.

[Still Waters]

Already posted.