March 24th, 2023 at 2:29:34 AM
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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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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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the foolish sayings of a rich man often pass for words of wisdom by the fools around him

March 24th, 2023 at 12:15:58 PM
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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.

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

So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.

March 24th, 2023 at 9:12:31 PM
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What am I not getting here? I see many tiles in repetition.

April 2nd, 2023 at 3:42:59 PM
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Quote:rainmanWhat am I not getting here? I see many tiles in repetition.

link to original post

Completely agree.

April 3rd, 2023 at 5:18:31 AM
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This YouTube video may help you to understand.Quote:rainmanWhat am I not getting here? I see many tiles in repetition.

link to original post

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.