lilredrooster
lilredrooster
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MentalWizard
March 24th, 2023 at 2:29:34 AM permalink
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4 mathematicians have discovered a 2 D shape that does not repeat itself when tiled - see link

tiling that does not have repeating patterns is known as aperiodic tiling

from the article:

"for many years mathematicians have been studying the idea of creating shapes that could be used to create an infinite variety of patterns when tiled"





https://phys.org/news/2023-03-geometric-tiled.html

https://kottke.org/23/03/a-potential-major-discovery-an-aperiodic-monotile


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gordonm888
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Dieter
March 24th, 2023 at 12:15:58 PM permalink
Fascinating.

I always feel that 2-dimensional geometry analysis is mostly a warm-up for working a problem in three dimensions. So I did some reading on 3-D tesselation/tiling.

I discovered the Johnson solid.

One of the Johnson solids, called a Schmitt–Conway–Danzer biprism, fills space with a "screw" symmetry and is indeed aperiodic. However it does not fully satisfy the criteria as a solution to the 3-D Einstein problem*.

* The Einstein problem is not named after Albert Einstein; rather Einstein is a German language word and means "one stone."

Johnson solid that fills space with a "screw" symmetry

Seemingly useless info, but I feel richer for knowing this.
Last edited by: gordonm888 on Mar 24, 2023
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rainman
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March 24th, 2023 at 9:12:31 PM permalink
What am I not getting here? I see many tiles in repetition.
Mukke
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April 2nd, 2023 at 3:42:59 PM permalink
Quote: rainman

What am I not getting here? I see many tiles in repetition.
link to original post



Completely agree.

EdCollins
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Mukkerainman
April 3rd, 2023 at 5:18:31 AM permalink
Quote: rainman

What am I not getting here? I see many tiles in repetition.
link to original post

This YouTube video may help you to understand.

https://www.youtube.com/watch?v=-eqdj63nEr4&t=34s

Basically, yes, you can have patches that repeat... but if you slide the whole thing up and around, it will never completely line up with itself again.
rxwine
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April 3rd, 2023 at 8:01:03 AM permalink
So, what happens if you use this for jigsaw puzzles? Harder, easier, no difference?
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